Question

A population culture begins with 15 strands of bacteria and then doubles every 4 hours. This can be modeled by 15(2)^t/4, where t is time in hours. How many strands of bacteria are present at 16 hours?

Question 14 options:

A)

300 strands of bacteria

B)

160 strands of bacteria

C)

225 strands of bacteria

D)

240 strands of bacteria

Answer 1

D. 240 strands of bacteria

Explanation:

Given a population culture modeled by the equation P(t) = 15(2)^t/4,

If the population culture begins with 15 strands of bacteria, at t = 0sec, P(t) = 15

if the population doubles after 4hours, this means a t = 4hrs, P(t) =2 * 15 = 30strands

We are to get P(t) when t = 16hours. Substituting t = 16 into the modeled equation we have;

P(16) = 15(2)^16/4

P(16) = 15(2)^4

P(16) = 15(16)

P(16) = 240 strands of bacteria.