91Ó°ÊÓ

Is it possible to write \(y\) as an exponential function of \(x\) ? Explain your reasoning. (Assume \(p\) is positive.) $$ \begin{array}{|c|c|} \hline \boldsymbol{x} & \boldsymbol{y} \\ \hline 1 & p \\ 2 & 2 p \\ 3 & 4 p \\ 4 & 8 p \\ 5 & 16 p \\ \hline \end{array} $$

Explain why \(A=P\left(1+\frac{r}{n}\right)^{n t}\) approximates \(A=P e^{r t}\) as \(n\) approaches positive infinity.

You invest \(\$ 500\) in the stock of a company. The value of the stock decreases \(2 \%\) each year. Describe and correct the error in writing a model for the value of the stock after \(t\) years.

Solve the equation. Check for extraneous solutions. \(\log _3(x-9)+\log _3(x-3)=2\)

Your friend evaluates \(f(x)=e^{-x}\) when \(x=1000\) and concludes that the graph of \(y=f(x)\) has an \(x\)-intercept at \((1000,0)\). Is your friend correct? Explain your reasoning.

Write a rule for \(g\) that represents the indicated transformation of the graph of \(f\). \(f(x)=\log _5 x\); reflection in the \(x\)-axis, followed by a translation 9 units left

Write a rule for \(g\) that represents the indicated transformation of the graph of \(f\). \(f(x)=\log _{1 / 2} x\); translation 3 units left and 2 units up, followed by a reflection in the \(y\)-axis

Use the given information to find the amount \(A\) in the account earning compound interest after 6 years when the principal is \(\$ 3500\).\(r=2.16 \%\), compounded quarterly

You invest $$\$ 2500$$ in an account to save for college. Account 1 pays \(6 \%\) annual interest compounded quarterly. Account 2 pays \(4 \%\) annual interest compounded continuously. Which account should you choose to obtain the greater amount in 10 years? Justify your answer.

ERROR ANALYSIS Describe and correct the error in simplifying the expression \(\log _4 64^x\). \(\begin{aligned} \log _4 64^x &=\log _4\left(16 \cdot 4^x\right) \\ &=\log _4\left(4^2 \cdot 4^x\right) \\ &=\log _4 4^{2+x} \\ &=2+x \end{aligned}\)