The population of a colony of bacteria can be modeled by the function P(t) = 19,300(5)t, where t is the elapsed time in hours. What is the inverse function? P–1(t) = 19,300 log5 (t) P–1(t) = log5 (19,300t) P–1(t) = log5 (StartFraction t Over 19,300 EndFraction) P–1(t) = 19,300 (One-fifth) Superscript t

Answer:

The inverse of the function is

P^-1(t) = Log5 t - Log5 19,300

or P^-1(t) = Log5 (t/19,300)

Step-by-step explanation:

Here, we want to find the inverse of the function.

Make t the subject of the formula, then solve the equation for P(t)

P(t) = 19,300(5)^t

Replace P(t) with t and t with P(t)

So we have

t = 19,300(5)^P(t)

Now make P(t) subject of formula

divide both sides by 19,300

t/19,300 = 5^p(t)

By logarithmic law:

Log5 (t/19,300) = P(t)

Hence P(t) = Log5 t - Log5 19,300

Now replace P(t) with P^-1(t)

So the inverse is;

P^-1(t) = Log5 t - Log5 19,300

Answer:

C)

Step-by-step explanation:

got it right on edge :)

Objects that are in the same plane are called _______________ . *

a company packages fruit baskets of different weights and ships them to customers. the company charges a flat fee for packaging the baskets. the total packaging and shipping cost in dollars, y, of a fruit basket weighing x pounds is represented by the line on the graph below. (1 point at (3, 10) another at (6, 16))
what is the y intercept of the line on the graph​

Solve 3(4x-1)=12x +7

Which table represents a linear function?
answers are in the picture plz help im timed​

40 POINTS FOR AWNSER

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.

Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation.


Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.


Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.


Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.


Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.

Erin drinks the same amount of milk every day. The equation below represents the proportional relationship between the number of gallons of milk (m) and the numbers of days (d) Erin drinks milk. 16m=2d How long does it take for Erin to drink 1 gallon of milk?

Tehara has read 115 pages of a 305 page book she reads 10 pages each day how many days will it take to finish

A poll conducted the day before the student- body presidential election at a midwestern university showed that 53.9 percent favored Mario, the rest favoring Yin Ling. The margin of error was 4.2 percentage points. Should Yin Ling have conceded the election?

Given m|n, find the value of x.
t
m
(9x+23)
(10x+6)°
Someone help?

¡¡. PLEASE HELP !!!!

how many snakeman and red crows were sold altogether

WILL RATE BRANLIEST Transversal t intersects lines a and b to form 8 angles. The angles formed with line a, clockwise from top left, are 1, 2, 3, 4. The angles formed with line b, clockwise from top left, are 5, 6, 8, 7.

For the diagram shown, which angles are corresponding angles

∠3 and ∠7

∠8 and ∠6

∠4 and ∠7

∠3 and ∠5

Let U = {q, r, s, t, u, V, W, X, y, z}
A = {q,S, U, W, y}
B = {q, s, y, z)
C = {v, w, x, y, z)
List the elements in the set.
A'UB

Her friend comes to the rescue and brings 15 more cups of chocolate chips! How many more muffins will they be able to make with the additional chocolate chips?

Which ordered pair gives the coordinates of a point that lies on the line shown in the graph?

The range of the x axis is minus five to five by increment of one. On the x axis minus four, minus two, two, and four are labeled. The range of the y axis is minus three to minus seven by increment of one. On the y axis minus two, two, four, and six are labeled. In the line graph, the x intercept of the line is (-2, 0) and y intercept of the line is (0, 4).

4. Write the equation of a line that passes through the point (-8, 2) and is parallel to the
line 3x – 2y = 12.​

x — бу + 2x = 5 2x – 3y+z = 4 3х +4y - z = -2


help on how to do it , its about substitution. ​

2.5 as a simplified fraction​

What is the value of h(3)?

find the coordinates of the midpoint of a segment with the given endpoints 3.)P(-12 -9) Q(2,10) help plz ​

Lili has saved $2,500 money from her part time job at a bakery. Since she will not need this money for a few years, she decides to put the money in a 3-year CD (Certificate of Deposit) at a local credit union. The credit union offers Lili 2.75% APR, compounded quarterly. How much will Lili's CD be worth at the end of the 3 years?

the level of detail that an instrument can measure is known as its _____

7. Evaluate the following expression for n = 4.
2n? - 8

I need help with 43. . . .

A goblin makes 50 pounds of goo in 2 hours. What is the unit rate?

19 is 50% of what number? round to the nearest tenth

Can you please help me? I will give brainliest, I appreciate it :) Thanks!

[(2r^2t)^3/4t^2]^2 simply

Solve for Y
-2х + 4y = 16
а. y = 2х + 4
b. у = -2х + 4
с. y = 1/2 х + 4
d. y = 1/2 x - 4

What is 13 / 143 as a unit fraction