Here we have a problem with exponential decays, we will find that we can expect that 110 rabbits will still be alive at the end of 7 days.
An exponential decay can be written:
P(x) = A*e^(-k*x)
Where:
A is the initial amount.
k defines the rate of decrease.
x is our variable.
In this case, the exponential decay is applied to the population of rabbits, and we know that:
The initial population is 240, then A = 240
P(x) = 240*e^(-k*x)
We also know that after two days (at x = 2) the population was 180, then we can write:
P(2) = 180 = 240*e^(-k*2)
With this equation we can find the value of k:
180 = 240*e^(-k*2)
180/240 = e^(-k*2)
Now remember that:
Ln(e^n) = n
then if we apply the natural logarithm to both sides, we get:
Ln(180/240) = Ln(e^(-k*2)) = -k*2
-Ln(180/240)/2 = k = 0.144
Then the equation is:
P(x) = 240*e^(-0.144*x)
Now with this, we can find the population of rabbits after 7 days, we just need to evaluate the above function at x = 7, we will get:
P(7) = 240*e^(-0.144*7) = 110.3
That we could round down to the next whole number, 110.
Concluding, we can expect that 110 rabbits will still be alive at the end of 7 days.
If you want to learn more, you can read:
https://brainly.com/question/14355665
