The population of goldfish in a marine farm is decreasing at the rate of 20 percent per year. The farm started with a goldfish population of 1,000. Part A

Create an equation that gives the number of goldfish in the nth year.

Step-by-step explanation:

Part A:

The equation modeling the problem is an exponential equation of the form:

y = A (b) * ^ t

Where,

A: initial amount

b: decrease rate

t: time

Substituting values we have:

y = 1000 (0.80) ^ t

Part B:

For this case we substitute the value of y = 640 in the equation:

640 = 1000 (0.80) ^ t

We cleared t:

640/1000 = (0.80) ^ t

log0.80 ((0.80) ^ t) = log0.80 (640/1000)

t = log0.80 (640/1000)

t = 2 years