Question

A sample of bacteria is decaying according to a half-life model. If the sample begins with 800 bacteria, and after 13 minutes there are 320 bacteria, after how many minutes will there be 15 bacteria remaining? Round your answer to the nearest whole number.

Answer 1

56.42 minutes

Explanation:

The initial sample= y0 = 800

After 13 minutes , amount = 320

Y= y0e-kt

320 = 800e-k(13)

320/800 = e-k13

0.4 = e-k13

In0.4 = -k13

-0.91629= -k13

0.07048= k

Y = 800e-0.07048t

Minutes when the bacterial present will be 15

15 = 800e-0.07048t

15/800= e-0.07048t

0.01875 = e-0.07048t

In 0.01875 = -0.07048t

-3.97656 = -0.07048t

-3.97656/-0.07048= t

56.42 = t

56.42 minutes