Question

The graph shows a population of butterflies, t weeks since their migration began.

c. Write an equation for the
population, q, after t weeks.

Answer 1

q = 250,000·(0.6^t)

Explanation:

You want an equation that models the graph of an exponential function that has an initial value of 250,000 and a value of 150,000 after 1 week.

Exponential function

An exponential function has the form ...

q = a·b^t

where 'a' is the initial value, and 'b' is the decay factor over a period of one time unit of t.

Application

The graph with this problem shows the initial value (for t=0) to be a=250,000. The decay factor will be ...

b = 150,000/250,000 = 3/5 = 0.6

Then the exponential function can be written as ...

q = 250000·(0.6^t) . . . . . . where t is in weeks