calc life science 14.1

Question

A population of bacteria follows the continuous exponential growth model P(t)=P0ekt​, where t is in days. The relative​ (daily) growth rate is 3.4​%. The current population is 838.

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

​P(t) =

​B) Find the population exactly 4 weeks from now.Round to the nearest

bacterium.The population in 4 weeks will be ___

.

​C) Find the rate of change in the population exactly 4 weeks from now.Round to the nearest

unit.The population will be increasing by about ___bacteria per day exactly 4 weeks from now.

​D) When will the popualtion reach 6514​? ROUND TO 2 DECIMAL

PLACES.The population will reach 6514

about ___days from now.

Answer 1

(A) P(t) = P₀e^kt

(B) 4 weeks is 28 days, P(28) = 838e^.034(28) = 2171

(C) .034(2171) = 73.8 bacteria per day

(D) 6514 = 838e^.034t 7.77=e^.034t ln7.77=.034t 60.3 days = t