Question

Suppose that the amount of algae in a pond doubles every 3 hours. If the pond initially contains 50 pounds of algae, how much algae will be in the pond after 8 hours.In this exponential situation, what would the y-intercept be? CHOICES:

(0,3)
(0,2)
(0,50)
(0,8)

Answer 1

After 8 hour there will be 317.64 pounds of algae.

y-intercept: (0, 50)

Explanation:

At time = 0 hours, there are 50 pounds of algae, after 3 hour there will be 100 pounds of algae, after 6 hour there will be 200 pounds of algae, and so on.

Exponential growth is modeled by the following equation:

y = x0*(1 + r)^t

where x0 is the amount of algae at the beginning, r is the rate of change, and y is the amount of algae after t hours. Replacing with data:

100 = 50*(1 + r)^3

2 = (1 + r)^3

ln(2) = 3*ln(1 + r)

r = exp(ln(2)/3) - 1

r = 0.26

This result can be checked as follows

y = 50*(1 + 0.26)^6 = 200

After 8 hours:

y = 50*(1 + 0.26)^8 = 317.64

The y-intercept corresponds to t = 0

y = 50*(1 + 0.26)^0 = 50