Question

A Galapagos cactus finch population increases by half every decade. The number of finches is

modeled by the expression 45 • 1.54, where d is the number of decades after the population
was measured. Evaluate the expression to find the number of finches for d=-2.

Answer 1

The number of fringes at
`d=-2` is given as 20.

Explanation:

Question

A Galapagos cactus finch population increases by half every decade. The number of finches is modeled by the expression

,

where d is the number of decades after the population was measured. Evaluate the expression for d = −2

Given :

The number of finches is modeled by the expression :

⇒
`45\cdot1.5^d`

where
`d` is the number of decades after the population was measured.

To evaluate the expression for d=-2

Solution:

In order to evaluate the given expression to find the number of finches at
`d=-2`, we will plugin
`-2` for
`d` in the expression and simplify it.

Plugging in
`d=-2` in the expression:

⇒
`45\cdot 1.5^(-2)`

Using negative exponent property. [
`a^(-x)=(1)/(a^x)`

⇒
`45\cdot (1)/(1.5^2)`

⇒
`45\cdot (1)/(2.25)`

⇒
`20` (Answer)

Thus, the number of fringes at
`d=-2` is given as 20.

This means the number of fringes two decades ago was 20.