The answer is:
In 2036 there will be a population of 32309 rabbits.
We can calculate the exponential decay using the following function:
[tex]P(t)=StartAmount*(1-\frac{percent}{100})^{t}[/tex]
Where,
Start Amount, is the starting value or amount.
Percent, is the decay rate.
t, is the time elapsed.
We are given:
[tex]StartAmount=144,000\\x=7.2(percent)\\t=2036-2016=20years[/tex]
Now, substituting it into the equation, we have:
[tex]P(t)=StartAmount(1-\frac{percent}{100})^{t}[/tex]
[tex]P(t)=144000*(1-\frac{7.2}{100})^{20}[/tex]
[tex]P(t)=144000*(1-0.072)^{20}[/tex]
[tex]P(t)=144000*(0.928)^{20}[/tex]
[tex]P(t)=144000*(0.928)^{20}[/tex]
[tex]P(t)=144000*0.861=32308.888=32309[/tex]
Hence, we have that in 2036 the population of rabbis will be 32309 rabbits.
Have a nice day!
The population of rabbits in 2036 is 32309 and this can be determined by using the exponential decay function.
Given :
The formula for the exponential decay function is given by:
[tex]\rm A = P(1-\dfrac{r}{100})^t[/tex]
Now, substitute the value of known terms in the above formula.
[tex]\rm A = 144000(1-\dfrac{7.2}{100})^{20}[/tex]
Simplify the above expression.
[tex]\rm A = 144000\times (0.928)^{20}[/tex]
[tex]\rm A = 32308.888[/tex]
A [tex]\approx[/tex] 32309
So, the population of rabbits in 2036 is 32309.
For more information, refer to the link given below:
https://brainly.com/question/11154952
