exponential decay 14.1

Question

A population of bacteria follows the continuous exponential growth model  

P(t)=P0e^kt​, where t is in days. The relative​ (daily) growth rate is 3.5​%. The current population is 483.

​A) Find the growth model.​ (the function that represents the population after t​ days).

​P(t) = ____

​

B) Find the population exactly 2 weeks from now.  Round to the nearest

bacterium.

The population in 2 weeks will be___

​

C) Find the rate of change in the population exactly 2

weeks from now. Round to the nearest

unit.

The population will be increasing by about ____ bacteria per day exactly 2

weeks from now.

​

D) When will the popualtion reach 5449​? ROUND TO 2 DECIMAL

PLACES.The population will reach 5449 about ___days from now.

Answer 1

0.035 = e^k, solve for k

A) P(t) = 483e^kt, using the value of k from above

B) P(14) = 483e^14k, using the value of k from above

C) Determine P'(t), Calculate P'(14)

D) 5449 = 483e^kt, using value of k from above and solving for t