Question

Two days after a biology experiment there was 49 million bacteria present. Four days after the experiment there was 600.25 million bacteria present. Find an exponential equation that models this situation. Shoe your work please!

Answer 1

y=Ae^(1.25t)

Explanation:

From the expression y=Ae^kt

After two days of the experiment, y = 49 million, t=2

After four days of the experiment, y= 600.25 million, t=4

A is the amount of bacteria present at time zero and t is the time after the experiment (in days)

At t=2 and y =49

49=Ae^2k…………….. (1)

At t=4 and y = 600.25

600.25=Ae^4k………… (2)

Divide equation (2) by equation (1)

600.25/49=(Ae^4k)/(Ae^2k )

12.25=e^2k

Take natural log of both sides

ln⁡(12.25) =2k

2.505⁡ =2k

k=1.25

The exponential equation that models this situation is y=Ae^(1.25t)