For the following exercises, consider this scenario: For each year $t$, the population of a forest of trees is represented by the function $A(t)=115(1.025)^t$. In a neighboring forest, the population of the same type of tree is Which forest had a greater number of trees initially? By how many?

For the following exercise,

Consider this scenario: For each year $t$, the population of a forest of trees is represented by the function $A(t)=115(1.025)^t$. In a neighboring forest, the population of the same type of tree is represented by the function $B(t)=82(1.029)^t$. (Round answers to the nearest whole number.)

Which forest had a greater number of trees initially? By how many?

For the following exercises, consider this scenario: For each year t, the population of a forest of trees is represented by the function $A(t)=115(1.025)^{t}.$ In a neighboring forest, the population of the same type of tree is represented by the function $B(t)=82(1.029)^{t}.$ (Round answers to the nearest whole number.) Which forest had a greater number of trees initially? By how many?

Suppose an investment account is opened with an initial deposit of $12,000 earning 7.2% interest compounded continuously. How much will the account be worth after 30 years?

Consider this scenario: For each year $t$, the population of a forest of trees is represented by the function $A(t)=115(1.025)^t$. In a neighboring forest, the population of the same type of tree is represented by the function $B(t)=82(1.029)^t$. (Round answers to the nearest whole number.)

Which forest had a greater number of trees initially? By how many?

For the following exercise,

Use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$.

Solve the compound interest formula for the principal, $P$.

For the following exercise,

Use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$.

Use properties of rational exponents to solve the compound interest formula for the interest rate, $r$.

You invest an amount of money at an annual simple interest rate of $6.25 \%$. You invest a second amount, $\$ 500$ less than the first, at an annual simple interest rate of $6 \%$. Let $x$ represent the amount invested at $6.25 \%$. Complete the following table.

Find the formula for an exponential function that passes through the two points given.

$(0,6)$ and $(3,750)$

Researchers studied the behavior of birds that were searching for seeds and insects in an Oregon forest. In this forest, 54% of the trees were Douglas firs, 40% were ponderosa pines, and 6% were other types of trees. At a randomly selected time during the day, the researchers observed 156 red-breasted nuthatches: 70 were seen in Douglas firs, 79 in ponderosa pines, and 7 in other types of trees. Do these data provide convincing evidence that nuthatches prefer particular types of trees when they're searching for seeds and insects?

Use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$.

Solve the compound interest formula for the principal, $P$.

For the following exercise, use the compound interest formula, $A(t)=P\left(1+\frac{r}{n}\right)^{n t}$.
After a certain number of years, the value of an investment account is represented by the equation $10,250\left(1+\frac{0.04}{12}\right)^{120}$. What is the value of the account?

A school's principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50 students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported per night. Explain carefully why it would not be appropriate to perform a chi-square test for goodness of fit using these data.

For the following exercise, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.\

$$y=300(1-t)^5$$