If f(x) is an exponential function where f(1.5) = 7 and f(8.5) = 46, then find the value of f(14), to the nearest hundredth.
Answers
Answer:
[tex]f(14)=201.932[/tex]
Step-by-step explanation:
Set up a system of equations and solve for "b"
[tex]\left \{ {{46=ab^{8.5}} \atop {7=ab^{1.5}}} \right\\ \\\left \{ {{\frac{46}{b^{8.5}}=a } \atop {\frac{7}{b^{1.5}}=a} \right\\\\\frac{46}{b^{8.5}}=\frac{7}{b^{1.5}}\\ \\46b^{1.5}=7b^{8.5}\\\\46=7b^7\\\\\frac{46}{7}=b^7\\ \\b=1.308604899[/tex]
Determine the value of "a" using "b"
[tex]y=ab^x\\\\46=a(1.308604899)^{8.5}\\\\46=9.837224985a\\\\a=4.676115477[/tex]
Find f(14) using the new function
[tex]f(x)=4.676115477(1.308604899)^x\\\\f(14)=4.676115477(1.308604899)^{14}\\\\f(14)\approx201.932[/tex]
Related Questions
Juanita has $25, and she makes $11 per hour. She needs at least $58 to buy new shoes. Write and solve an inequality to determine how many hours Juanita must work to be able to buy new shoes. Then interpret the solution.
Answers
Answer:
Juanita must work 3 hours and above to be able to buy new shoes.
Step-by-step explanation:
Initially, Juanita has $25 and make $11 per hour
meaning, Juanita's new cash in hand after t hours is;
[tex]\tt C=25+11t[/tex]
Juanita needs at least $58 to buy new shoes;
meaning, the minimum cash Juanita should have should be $58 and above.
Simply put,
[tex]\tt C\geq 58[/tex]
[tex]---> \tt 25+11t\geq 58[/tex]
[tex]\tt --->11t\geq 58-25[/tex]
[tex]---> \tt 11t\geq 33[/tex]
[tex]----> \tt t\geq \frac{33}{11}[/tex]
[tex]---> \tt t>3[/tex]
The solution reveals that Juanita must work 3 hours and above to be able to buy new shoes.
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which variable is ordinal?
Answers
Answer:
Categorical variable
Step-by-step explanation:
An ordinal variable is a categorical variable for which the possible values are ordered. Please mark me as brainliest.
PLEASE HELP ASAP
How much did the borrower pay for county taxes?
O A. $500.00
O B. $605.36
O C. $1,000.00
O D. $1,210.72
Answers
Taxes are rates or amount deducted from individuals.
The borrower paid $605.36 for county taxes
How to determine the amount paidFrom the table, we have the following entry:
County taxes (half year) (6) $605.36
The above represents the amount paid for county taxes
Hence, the borrower paid $605.36 for county taxes
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Answer:
$605.36
$605.36
$605.36
$605.36
$605.36
$605.36
Kala is riding her bike. She rides at a speed of 13 kilometers per hour for 32.5 kilometers. How many hours does she ride?
Answers
Answer:
32.5/13=time=2.5h
Time=distance /speed
To find the volume of the triangular prism first find the area of the triangular base
Answers
Answer:
Socratic app
Step-by-step explanation:
it will help you
A basketball team lost 10% of the games they played. They played 30 games in all. How many games did they win?
Answers
Answer:
They won 27 games
Step-by-step explanation:
10% of 30 is 3,
so 30-3= 27
PLEASE HELP ME
22 thousands, 22 hundreds,
222 tens
Answers
Numbers can be represented using the place value system
The number 22 thousands, 22 hundreds, 222 tens represents 26420
How to calculate the numberThe number is given as:
22 thousands, 22 hundreds, 222 tens
Rewrite the number as:
22 thousands + 22 hundreds + 222 tens
Express the place values as figures
22 * 1000 + 22 * 100 + 222 * 10
Evaluate the product
22000 + 2200 + 2220
Evaluate the sum
26420
Hence, 22 thousands, 22 hundreds, 222 tens represents 26420
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-4.56 × 10-3 in standard form.
Answers
Answer:
-48.6
Step-by-step explanation:
Find the odds of an event occurring, given the probability 1/2
Answers
can yall please help me
Answers
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] ÷ 4 = [tex]\frac{1}{3}[/tex] x [tex]\frac{1}{4}[/tex] = [tex]\frac{1}{12}[/tex]
When you have a fraction divide a number, you need to multiple it's reciprocal
Answer: 1/12
Step-by-step explanation:
1/3 x 1/4= 1/12
4/1 is flipped when switching from division ton multiplication
does 1\2 = 2\3 or would it 1\2 ≤ 2\3
Answers
Answer:
1/2 < 2/3
Step-by-step explanation:
1/2 = .5 in decimal form while 2/3 is .6 repeating in decimal form
1/2 < 2/3
*Watch image for better understanding
Blue portion is 1/2
Red portion is 2/3
so, obviously red portion is bigger than blue one.
The ratio of students who made
the honor roll to the total number
of students is 1:50) If there are
500 students in total, how many
made the honor roll?
Answers
Answer:
10
Step-by-step explanation:
1 out of 50 got it, so 500/50=10
Answer:
10 students
Step-by-step explanation:
if the ratio is 1:50 and there are 500 kids then you multiply the 50 by 10 to make it 500 then you also multiply the 1 by to so only 10 kids made honor roll
Help me plzzzz
I need to turn this in plz help me
Answers
Answer:
75 miles
Step-by-step explanation:
Answer:
75 miles
Step-by-step explanation:
20 miles = 1 gallon of gas
3 3/4 = 15/4
12/4 = 3 = 3 x 20 = 60 miles
3/4 of 20 = 15 miles
60 + 15 = 75 miles
What is the slope of the function given in the graph above?
A 4
B 3
C 6
Plsss helppp
Answers
Answer:
3
Step-by-step explanation:
I think it's 3
but I don't know if it's correct I just think it's 3
15b^(9/5) + 9b^(4/5)
Factor completely.
Answers
Answer:
3b^(4/5) * (5b + 3)
Step-by-step explanation:
Factor:
[tex]15b^{9/5} + 9b^{4/5}[/tex]Take out the factor 3b^4/5
[tex]3b^{4/5}(5b) + 3b^{4/5}(3)[/tex][tex]3b^{4/5}(5b + 3)[/tex]-Chetan K
Give the scale factor from figure A to figure B. Use / for fractions.
Answers
B to A is 1.5
A chocolate chip cookie recipe ask for one and one half times as much flour as chocolate chips. If three and three quarters cups of flour is used what quantity of chocolate chips would then be needed according to the recipe?
Answers
hahahahahahahhahahahahah
Christopher has a collection of 20 video games and will buy 4 more each month. Peter has a collection of 92 video games and will sell 5 each month. After how many months will they have the same number of video games? How many will that be?
Answers
Answer:
20 + 4 = m 92 - 5 = m
Step-by-step explanation:
due the the fact that theres no number for how meny months there are
factorise 18x-6
will give brainly to whoever answers first
Answers
Answer:
6(3x-1)
Step-by-step explanation:
They both have a common factor of 6
So divide 6 and take it out to give:
6(3x-1)
Solve each simple interest word problem 11) A new car volued at $28.000, depreciates of 9% per year. What is the value of the car one year after purchase?
Answers
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &28000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=\textit{elapsed time}\dotfill &1 \end{cases} \\\\\\ A=28000(1-0.09)^1\implies A=28000(0.91)\implies A=25480[/tex]
Answer:
$25,480
Step-by-step explanation:
In one year, the car depreciates by 9% of its original value:
0.09 × $28,000 = $2520 . . . . amount of depreciation
The value at the end of one year is ...
$28,000 -2,520 = $25,480
The value one year after purchase is $25,480.
h + 169 = 759 solve for h
Answers
Answer:
h = 590
Step-by-step explanation:
To find x, rearrange the equation to where h is on its own side.
Rearranged equation:
[tex]759 - 169 = h[/tex]
Since 169 added to h was to find 769, 169 subtracted from 759 represents h.
Solve:
[tex]759 - 169 = 590[/tex]
590 = h.
3.1721 x 10⁻⁷
Write this in standard notion
Answers
Basically -7 indicates to put 7 zeros in front of the number 3.1721
Find the value of x.
Answers
Answer:
x= 96
Step-by-step explanation:
an triangles angles always add up to 180 so 44+40 equals 84 and 180-84= 96.
100kg of potatoes are given to 100 people. Each adult gets 3kg, each teenager gets 2kg and each small child gets 0.5kg. How many adults and teenagers and small children were there?
Answers
Answer:
there are 18 Adults 18 Teenagers and 20 small children
(10 points) Chip made his eggnog recipe which was 12% sugar, but it was not sweet enough for Dale. Dale made his recipe which was 20% sugar, but it was too sweet for Chip. How much of each eggnog do they need to mix to get 80 oz. of eggnog which has15% sugar concentration?
Answers
50 oz. of 12% sugar and 30 oz. of 20% sugar is needed to produce 80 oz. of 15% sugar.
EquationAn equation is an expression used to show the relationship between two or more numbers and variables.
Let x represent the amount of 12% sugar and y represent the amount of 20% sugar need to produce 80 oz. of 15% sugar. Hence:
x + y = 80 (1)
Also:
0.12x + 0.2y = 0.15(80) (2)
From both equations:
x = 50, y = 30
50 oz. of 12% sugar and 30 oz. of 20% sugar is needed to produce 80 oz. of 15% sugar.
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Find the height of an equilateral triangle of side 6 cm
Answers
Answer:
Answer: The height of the given equilateral triangle is 3√3 cm.
someone please help me!
Answers
Answer:
x = 14
Step-by-step explanation:
All angles add up to 180
2x - 5 + 3x - 8 + 10x - 17 = 180
Combine like terms and solve
x = 14
Consider the equation y = 3x - 1
Identify the slope and y-intercept and
sketch the graph.
Answers
If you want to find the y-intercept, you do that by putting a zero in for x, so you want to find the point that the line intersects the y-axis. So x would be zero, and wherever that point is is the y-intercept. In this case:
y = 3x - 1
y = 3(0) - 1
3 times 0 is zero
y = - 1 So, the y-intercept is - 1, or (0,-1)
To sketch the graph, you just place any number in for x or y (x is easier in this case), and solve it.
For example, I am going to say that x equals two.
y = 3(2)-1
y = 6-1
y = 5
So, your point to put on the graph would be (2,5) (x,y)
There is something that, although it belongs to you, people always use it more than you. What is it?
Answers
Answer:
Your name is the answer to the riddle.
C
On Wednesday they made $5.50 How much does Zara get?
Please help?
Answers
Answer
Zara gets $5.50
Step-by-step explanation: