Question

Researchers recorded that a certain bacteria population declined from 100,000 to 100 in 24 hours. At this rate of decay, how many bacteria would there have been at 16 hours from the start of the experiment? Use exact values in your calculations and do not round in intermediate steps. Your final answer should be a whole number ending in one or more zeros.

Answer 1

Answer:

A = 1013.25

Explanation:

First we will find the rate of decrease of population of bacteria

As we know that

$A = A_0*e^{kt}$

Where A is the final population

$A_0 =$ the initial population

K is the rate of decrease of population

t is the time period

Substituting the given values, we get -

$100 = 100,000 * e ^{k *24}$

$10^{-3} = e^{k*24}$

taking antilog on both sides, we get -

- 6.907 = k *24

k = -0.287 /hr

Now,

After 16 hour the population would be

$A = 100,000 * e*{-0.287*16}\\A = 1013.25$