In a pond, the area that is covered by algae doubles each week. When the algae is first spotted, the area it covered is about 12.5 square meters.

1. Explain why we can find the area covered by algae 1 day after it was spotted by multiplying 12.5 by \(\sqrt[7]{2}\).
2. Find the area, in square meters, covered by algae 10 days after it is spotted. Show your reasoning.

The function \(m\), defined by \(m(h) = 300\boldcdot\left(\frac34\right)^h\), represents the mass of material left, in milligrams, \(h\) hours after it is measured.

1. What does \(m(0.5)\) represent in this situation?
2. This graph represents the function \(m\). Use the graph to estimate \(m(0.5)\).

   

3. Suppose the material is measured at noon. Use the graph to estimate the amount of material left at 4:30 p.m. on the same day.

The area covered by a lake is 11 square kilometers. It is decreasing exponentially at a rate of 2 percent each year and can be modeled by \(A(t)=11 \boldcdot (0.98)^t\).

1. By what factor does the area decrease in 10 years?
2. By what factor does the area decrease each month?

A sequence of numbers is increasing exponentially. Write the first two numbers of the sequence.

\(\underline{\hspace{.5in}}, \underline{\hspace{.5in}}, 100, 500\)

The population of a city in thousands is modeled by the function \(f(t) = 250 \boldcdot (1.01)^t\), where \(t\) is the number of years after 1950. Which of these statements are true for the model? Select all that apply.