Question

A certain bacteria population increases continuously at a rate proportional to its current number. The initial population of the bacteria is 70. The population increases to 360 bacteria in 4 hours. Approximately how many bacteria are there in 7 hours? Round your answer to the nearest whole number.

Answer 1

Answer: C

Explanation:

This describes an expotential function

At t = 0, P = 70

Therefore, C = 70

P = 70 e^kt

Solve for k by plugging in (4,360)

k = 0.4094

plug in t(7 hours)

70 e^(0.4094*7)

The answer roughly equals C

Answer 2

C

Explanation:

B = 70 × r^t

360 = 70 × r⁴

r⁴ = 36/7

4lnr = ln(36/7)

lnr = 0.4094021974

r = e^0.4094021974

r = 1.505917275

At t = 7,

B = 70 × (1.505917275)⁷

B = 1229.435775

Approximately 1229