Question

1. choose the correct answers.

in 1995, wildlife biologists found that in any given hour at a particular beach, there were 5,750 mosquitoes present. they also found that the population of mosquitoes was tripling each year.
write an exponential equation to model the population change in mosquitoes at this beach.
using this model, how many mosquitoes were present on this beach at any hour in 2008?
a. $a(t) = 5,750(3)^t$
b. $a(t) = 5,750(4)^t$
c. 9,167,357,250 mosquitoes
d. 47,104,000 mosquitoes
e. $a(t) = 5,750(2)^t$

Explanation:

Step1: Identify exponential model form

The general exponential growth model is $A(t) = A_0(r)^t$, where $A_0$ is the initial amount, $r$ is the growth factor, and $t$ is time in years.

Step2: Plug in known values

Initial population $A_0=5750$, growth factor $r=3$ (tripling yearly). So $A(t)=5750(3)^t$.

Step3: Calculate time elapsed

$t = 2008 - 1995 = 13$ years.

Step4: Compute 2008 population

Substitute $t=13$ into the model: $A(13)=5750(3)^{13}$. First calculate $3^{13}=1594323$, then $5750\times1594323=9167357250$.

Answer:

a. $A(t) = 5, 750(3)^t$
c. 9, 167, 357, 250 mosquitoes