Question

4 A group of 40 mountain goats has just been

transplanted to an area with the expectation
their population will increase exponentially by
30% each year. If f(x) represents their total
population and x is the number of years in the
future, which function models the situation?

Answer 1

f(x) = 40 × (1.3)ˣ

Explanation:

4. The given parameters of the population of mountain goats are;

The initial number of mountain goats, a = 40

The rate at which their population will increase, r = 30% = 0.3 exponentially

The total population after 'x' years is given by f(x)

For exponential growth, we have;

f(x) = a·(1 + r)ˣ

Plugging in the values, we get;

f(x) = 40 × (1 + 0.3)ˣ = 40 × (1.3)ˣ