sat-dog

Choice B is correct. Since the model estimates that the number of squirrels in the population increased by a fixed percentage, $150\%$, each year, the model can be represented by an exponential equation of the form $n=a{\left(1+\frac{p}{100}\right)}^t$, where $a$ is the estimated number of squirrels in the population at the end of $2015$, and the model estimates that at the end of each year, the number is $p\%$ more than the number at the end of the previous year. Since the model estimates that at the end of each year, the number was $150\%$ more than the number at the end of the previous year, $p=150$. Substituting $150$ for $p$ in the equation $n=a{\left(1+\frac{p}{100}\right)}^t$ yields $n=a{\left(1+\frac{150}{100}\right)}^t$, which is equivalent to $n=a{\left(1+1.5\right)}^t$, or $n=a{\left(2.5\right)}^t$. It’s given that the estimated number of squirrels at the end of $2016$ was $180$. This means that when $t=1$, $n=180$. Substituting $1$ for $t$ and $180$ for $n$ in the equation $n=a{\left(2.5\right)}^t$ yields $180=a{\left(2.5\right)}^1$, or $180=2.5a$. Dividing each side of this equation by $2.5$ yields $72=a$. Substituting $72$ for $a$ in the equation $n=a{\left(2.5\right)}^t$ yields $n=72{\left(2.5\right)}^t$.

Choice A is incorrect. This equation represents a model where at the end of each year, the estimated number of squirrels was $150\%$ of, not $150\%$ more than, the estimated number at the end of the previous year.

Choice C is incorrect. This equation represents a model where at the end of each year, the estimated number of squirrels was $150\%$ of, not $150\%$ more than, the estimated number at the end of the previous year, and the estimated number of squirrels at the end of $2015$, not the end of $2016$, was $180$.

Choice D is incorrect. This equation represents a model where the estimated number of squirrels at the end of $2015$, not the end of $2016$, was $180$.