Question

Two researchers are studying the decline of orangutan populations. In one study, a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year. In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year. After how many years will the two populations be the same?

Answer 1

Answer: 3 years

Step-by-step explanation:

Answer 2

Write two functions that describes the decrease of the population after t years.

1.  In one study, a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year. Then after t years the number of orngutans will be

$y=784-25t.$

2.  In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year. Then after t years the number of orngutans will be

$y=817-36t.$

3. Equate right sides of the equations:

$784-25t=817-36t,\\ \\36t-25t=817-784,\\ \\11t=33,\\ \\t=3\ years.$

Answer: after 3 years