91Ó°ÊÓ

Population of Nevada Table 1.9 gives the population of Nevada for several years. Population of Nevada $$\begin{array}{ll}{\text { Year }} & {\text { Population (thousands) }} \\\ {1998} & {1,853} \\ {1999} & {1,935} \\ {2000} & {1,998} \\ {2001} & {2,095} \\ {2002} & {2,167} \\ {2003} & {2,241}\end{array}$$ (a) Compute the ratios of the population in one year by the population in the previous year. (b) Based on part (a), create an exponential model for the population of Nevada. (c) Use your model in part (b) to predict the population of Nevada in \(2010\).

Population of Virginia Table 1.10 gives the population of Virginia for several years. Population of Virginia $$\begin{array}{ll}{\text { Year }} & {\text { Population (thousands) }} \\\ {1998} & {6,901} \\ {1999} & {7,000} \\ {2000} & {7,078} \\ {2001} & {7,193} \\ {2002} & {7,193} \\ {2003} & {7,386}\end{array}$$ (a) Compute the ratios of the population in one year by the population in the previous year. (b) Based on part (a), create an exponential model for the population of Virginia. (c) Use your model in part (b) to predict the population of Virginia in \(2008\).

Population Growth The population of Silver Run in the year 1890 was 6250 . Assume the population increased at a rate of 2.75\(\%\) per year. (a) Estimate the population in 1915 and \(1940\). (b) Approximately when did the population reach \(50,000 ?\)

In Exercises \(17-22,\) specify (a) the period, (b) the amplitude, and (c) identify the viewing window that is shown. $$y=\cos \pi x$$

In Exercises \(21-24,\) write a general linear equation for the line through the two points. $$(1,1), \quad(2,1)$$

Radioactive Decay The half-life of phosphorus- 32 is about 14 days. There are 6.6 grams present initially. (a) Express the amount of phosphorus-32 remaining as a function of time \(t\). (b) When will there be 1 gram remaining?

Finding Time If John invests \(\$ 2300\) in a savings account with a 6\(\%\) interest rate compounded annually, how long will it take until John's account has a balance of \(\$ 4150\)?

Doubling Your Money Determine how much time is required for an investment to double in value if interest is earned at the rate of 6.25\(\%\) compounded annually.

In Exercises \(21-30\) , determine whether the function is even, odd, or neither. Try to answer without writing anything (except the answer). $$y=x+x^{3}$$

In Exercises \(25-26,\) show that the function is one-to-one, and graph its inverse. $$y=\tan x\( \)-\frac{\pi}{2}\( \)< x <$$\frac{\pi}{2}$$