Question

The deer population in the united states can be predicted by the expression 523(1.099)^t where t is the number of years since 1990 . what does the value 523 represent?

Answer 1

Step-by-step explanation:

The exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the following form:

`f(x)=a(1+r)^x`

or

`f(x)=ab^x\text{ where b= 1+r}`

here

a is the initial or starting value of the function or initial population.

r is the percent growth or decay rate, written as a decimal

and

b is the growth factor or growth multiplier.

Now, consider the following exponential model:

`f(t)=523\left(1.099\right)^t`

notice that in this case:

a = 523

according to the definition of exponential growth, we can conclude that the correct answer is:

Answer:

523 is the initial population of deers.