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

Answer:

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

Step-by-step 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. [$a^{-x}=\frac{1}{a^x}$

⇒ $45\cdot \frac{1}{1.5^2}$

⇒ $45\cdot \frac{1}{2.25}$

⇒ $20$   (Answer)

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

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