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Magazine Problem 57
Graph the exponential function. $$y=\left(\frac{1}{3}\right)^{x}$$
Problem 57
SIZE OF JUPITER Jupiter, the largest planet in our solar system, has a radius of about \(4.4 \times 10^{4}\) miles. Use the equation \(V=\frac{4}{3} \pi r^{3}\) to find Jupiter's volume.
Problem 58
Graph the exponential function. $$y=\left(\frac{1}{5}\right)^{x}$$
Problem 58
In Exercises \(58-60\), use the following information. In \(1803,\) the Louisiana Purchase added \(8.28 \times 10^{5}\) square miles to the United States. The cost of this land was \(\$ 15\) million. In \(1853,\) the Gadsden Purchase added \(2.94 \times 10^{4}\) square miles, and the cost was \(\$ 10\) million. Find the average cost of a square mile for each of the purchases.
Problem 59
Graph the exponential function. $$y=4^{-x}$$
Problem 59
Then evaluate the expression when \(a=1\) and \(b=2\). $$ \left(a \cdot b^{2}\right)^{2} $$
Problem 60
Graph the exponential function. $$y=5^{x}$$
Problem 60
You roll a die eight times. What is the probability that you will roll eight sixes in a row?
Problem 60
Then evaluate the expression when \(a=1\) and \(b=2\). $$ \left(a^{2} b\right)^{4} $$
Problem 60
In Exercises \(58-60\), use the following information. In \(1803,\) the Louisiana Purchase added \(8.28 \times 10^{5}\) square miles to the United States. The cost of this land was \(\$ 15\) million. In \(1853,\) the Gadsden Purchase added \(2.94 \times 10^{4}\) square miles, and the cost was \(\$ 10\) million. Writing Describe a factor that you think might explain the difference in the price per acre for these two purchases.
