Question

A population of bears is decreasing the population this year is 200 bears after 1 year it is estimated that the population will be 160 bears after 2 years it is estimated that the population will be 128 bears what equation describes the bear population in any year x?

Answer 1

The equation is;

y = 200•0.8^x

where y is the number of bears remaining and x is the year number in particular

Explanation:

Let us have the rate of decrease as r and we set up an exponential equation

y = I• ( 1 - r)^x

where r is the percentage decrease, I is the initial population = 200 and x is the number of years

For the population after 1 year, we have;

160 = 200( 1 -r)^x

divide both sides by 200

0.8 = (1-r)^1

0.8 = 1 - r

r = 1 - 0.8

r = 0.2

So the equation will be;

y = 200( 1 - 0.2)^x

y = 200•0.8^x