Question

The population of a rare species of fish, in thousands, is modeled by the linear functionf(t) = 137.618 +2.514t where t represents the time, in years, since 2018. Use this linear model toestimate the population of fish in the year 2035.

Answer 1

Given the population of a rare species of fish, in thousands, is modeled by the linear function

f(t) = 137.618 +2.514t

t is the time since 2018

We want to estimate the population of fish in the year 2035, to do that we must first know the number of years between 2018 and 2035

t = 2035 - 2018

t = 17

Substitute t = 17 into the modeled function as shown;

f(t) = 137.618 +2.514t

f(17) = 137.618 +2.514(17)

f(17) = 137.618 + 42.738

f(17) = 180.356

Hence the approximate value of the population in 2035 will be 180populations.