A farmer decides to enclose a rectangular garden using the side of a barn as one side of the rectangle. What are the maximum dimensions that can be enclosed with 80 ft of fence? What is the maximum area of this garden? Select the correct choice below and fill in the answer box(s) to complete your choice. A. The area is maximized when both sides are \( \square \mathrm{nt} \). The area is maximized when the longer side is \( \square \mathrm{ft} \) and the shorter side is The maximum area that the farmer can enclose with 80 ft of fence is \( \square \mathrm{sq} \mathrm{ft} \)

The size of a certain insect population is given by \( \mathrm{P}(\mathrm{t})=400 e^{.03 \mathrm{t}} \), where t is measured in days. At what time will the population equal 1600 ?

The function \( f(t)=60,000(2)^{\frac{1}{40}} \) gives the number of bacteria in a population \( t \) minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

Use the graph to evaluate the following expressions. (a) \( (\mathrm{f} \circ \mathrm{g})(1) \) (b) \( (\mathrm{g} \circ \mathrm{f})(0) \) (c) \( (\mathrm{g} \circ \mathrm{g})(0) \) (a) Evaluate \( (\mathrm{f} \circ \mathrm{g})(1) \). ( \( \mathrm{f} \circ \mathrm{g})(1)=1 \) (b) Evaluate \( (\mathrm{g} \circ \mathrm{f})(0) \). ( \( \mathrm{g} \circ \mathrm{f})(0)=0 \) (c) Evaluate \( (\mathrm{g} \circ \mathrm{g})(0) \). ( \( \mathrm{g} \circ \mathrm{g})(0)=0 \)

Determine the implied domain of the following function. Express your answer in interval notation. \[ f(x)=\sqrt{x}-9 \] Answer

Use the remainder theorem to find the remainder when \( f(x) \) is divided by \( x-1 \). Then use the factor theorem to determine whether \( x-1 \) is a factor of \( f(x) \). \( f(x)=2 x^{4}+7 x-3 \) The remainder is