10 points and i will give brainliest
9. a biologist is researching a newly-discovered species of bacteria. at time t = 0 hours, he puts seventy-five bacteria into what he has determined to be a favorable growth medium. four hours later, he measures 325 bacteria. assuming exponential growth, what is the growth constant "k" for the bacteria? (round k to two decimal places.)

Step-by-step explanation:

A biologist is researching a newly-discovered species of bacteria.

at time t=0 hours, he puts one hundred bacteria into what he has determined to

be a favorable growth medium.

Six hours later, he measures 450 bacteria.

Find an exponential equation that approximates the information.

:

find k, the growth factor

100*(2^(6/k)) = 450

Divide both sides by 100

2^(6/k) = 4.5

use logs here

log(2^(6/k)) = log(4.5)

:

log(2) = log(4.5)

=  

= 2.17

k =  

k = 2.765 is the growth factor

:

A = Ao*2^(t/2.765), the exponential equation

where

Ao = initial amt

A = amt after t hrs

1 . x = 9,

2 . n = 4,

3 . Clare made an error in the 2nd step; Correct answer is y = - 65 / 11

Step-by-step explanation:

1 .

2 .

3 . Clare made an error in the second step ( 72 + 24y = 4y - 5 - 9y ) and to derive the correct solution, see the following steps below;