Question

the population P of a bacteria culture is modeled by P=4300e^kt, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double?

Answer 1

93 h

Explanation:

P = 4300eᵏᵗ

1. Calculate the value of k

lnP = ln4300 + kt

ln5800 = ln4300 + k(40 h)

8.666 = 8.366 + 40k h

8.666 - 8.366 = 40k h

0.299 = 40 k h

k= 0.299/40 h = 7.481 × 10⁻³ h⁻¹

2. Calculate the time for the population to double

2 × 4300 = 4300eᵏᵗ

2 = eᵏᵗ

ln2 = kt

t = ln2/k = ln2/(7.481 × 10⁻³ h⁻¹) = 93 h

It takes 93 h for the population to double.