For a given initial quantity A, a decrease of x% can be written as:
A - A*(x%/100%) = A*(1 - x%/100%)
With this, we need to construct an exponential decrease equation for the given situation, and we will find that the equation is:
P(t) = 300*(0.77)^t
Now let's see how we found that.
In this case, we know that:
The initial number of animals is 300.
They decrease at an anual rate of 23%.
This means that after the first year, the population will be:
P(1) = 300 - 300*(23%/100$) = 300*( 1 - 0.23) = 300*(0.77)
After another year, the population decreases again, so we get:
P(2) = 300*(0.77) - 300*(0.77)*(23%/100$) = 300*(0.77)^2
Here we already can see the pattern, the population in the year t, we will get:
P(t) = 300*(0.77)^t
Then we can see that the correct option is C.
If you want to learn more, you can read:
https://brainly.com/question/16993154
