91Ó°ÊÓ

In Problems \(1-3,\) find the following: (a) \(\quad f(g(x))\) (b) \(g(f(x))\) (c) \(f(f(x))\) $$f(x)=x-2 \text { and } g(x)=x^{2}+8$$

Each of the following functions gives the amount of a substance present at time \(t .\) In each case, give the amount present initially (at \(t=0\) ), state whether the function represents exponential growth or decay, and give the percent growth or decay rate. (a) \(\quad A=100(1.07)^{t}\) (b) \(\quad A=5.3(1.054)^{t}\) (c) \(\quad A=3500(0.93)^{t}\) (d) \(\quad A=12(0.88)^{t}\)

Determine whether or not the function is a power function. If it is a power function, write it in the form \(y=k x^{p}\) and give the values of \(k\) and \(p\) $$y=5 \sqrt{x}$$

The exponential function \(y(x)=C e^{\alpha x}\) satisfies the conditions \(y(0)=2\) and \(y(1)=1 .\) Find the constants \(C\) and a. What is \(y(2) ?\)

Use the description of the function to sketch a possible graph. Put a label on each axis and state whether the function is increasing or decreasing. The amount of carbon dioxide in the atmosphere is a function of time, and is going up over time.

Suppose \$ 1000\( is invested in an account paying interest at a rate of \)5.5 \%$ per year. How much is in the account after 8 years if the interest is compounded (a) Annually? (b) Continuously?

In Problems \(1-3,\) find the following: (a) \(\quad f(g(x))\) (b) \(g(f(x))\) (c) \(f(f(x))\) $$f(x)=3 x \text { and } g(x)=e^{2 x}$$

Determine whether or not the function is a power function. If it is a power function, write it in the form \(y=k x^{p}\) and give the values of \(k\) and \(p\) $$y=\frac{8}{x}$$

Find an equation for the line that passes through the given points. $$(-2,1) and (2,3)$$

Graph the function. What is the amplitude and period? $$y=-3 \sin 2 \theta$$