You deposit \(\$500\) in an account with an annual interest rate of \(8\%\) compounded continuously. Find an equation that gives the amount of money in the account after \(t\) years, the amount in the account after \(5\) years.

Mini Lecture
If \(f(x)=3^x\) and \(g(x)=\left(\displaystyle\frac{1}{2}\right)^x\), find:

1. \(g(0)\)

2. \(f(-3)\)

3. \(f(2)+g(-2)\)

4. Graph \(y=2^x\)

5. Graph \(y=3^x\) and its inverse.

Mini Lecture

1. Find the inverse and graph the function \(f(x)=3x-1\).

2. Graph \(y=x^2-3\) and its inverse.

3. Graph \(y=3^x\) and its inverse.

4. Find the inverse \(f(x)=\displaystyle\frac{2x+1}{3x+1}\)

Mini Lecture

Solve for \(x\).

\(1\). \(\log_3 x = 2\) \(2\). \(\log_8 2 = x\)

\(3\). Graph \(y = \log_2 x\)

Simplify.

\(4\). \(\log_2 16\) \(5\). \(\log_3 3\) \(6\). \(\log_5 1\) \(7\). \(\log_3( \log_6 6)\)

Mini Lecture
Find on a calculator.

1. \(\log 378\)

2. \(\log 0.378\)

3. \(\ln 378\)

4. \(\ln e\)

Find \(x\).

5. \(\log x=2.8802\)

6. \(\log x=1.8802\)

7. \(\ln x=2.8802\)

Evaluate \(\log_3 7\) from the graph.

Mini Lecture
Solve.

1. \(3^x=5\)

2. \(3^{2x+1}=2\)

3. \(4^{x+1}=4\)
   

Evaluate.

4. \(\log_8{16}\)

5. \(\log_7{15}\)

Graph: \(g(x)=3^{-x}\)

Sketch the graph and find its inverse: \[f(x)=2x-3\]

Sketch the graph and find its inverse: \[f(x)=x^2-4\]

Solve for \(x\): \[\log_4 x=3\]

Solve for \(x\): \[\log_x 5=2\]

Graph: \[y=\log_{\frac{1}{2}}x\]

Evaluate: \[\log_8 4\]

Evaluate: \[\log_7 21\]

Evaluate: \[\log 23,400\]

Evaluate: \[\log 0.0123\]

Evaluate: \[\log 0.0123\]

Evaluate: \[\ln 0.0462\]

Use the properties of logarithms to expand: \[\log_2 \frac{8x^2}{y}\]

Use the properties of logarithms to expand: \[\log \frac{\sqrt{x}}{\left(y^4\right)\sqrt[5]{z}}\]

Write as a single logarithm: \[2\log_3 x-\frac{1}{2}\log_3 y\]

Write as a single logarithm: \[\frac{1}{3}\log x-\log y-2\log z\]

Use a calculator to find \(x\): \[\log x=4.8476\]

Use a calculator to find \(x\): \[\log x=-2.6478\]

Solve for \(x\): \(5=3^x\)

Solve for \(x\): \(4^{2x-1}=8\)

Solve for \(x\): \[\log_5 x-\log_5 3=1\]

Solve for \(x\): \[\log_2 x-\log_2(x-7)=3\]

Find the pH of a solution in which \(\left[\text{H}^+\right]=6.6\times 10^{-7}\)

If \(\$400\) is deposited in an account that earns \(10\%\) annual interest compounded twice a year, how much money will be in the account after \(5\) years?

How long will it take \(\$600\) to become \(\$1,800\) if the \(\$600\) is deposited in an account that earns \(8\%\) annual interest compounded \(4\) times a year?

If a car depreciates in value \(20\%\) per year for the first \(5\) years after it is purchased for \(P_0\) dollars, then its value after \(t\) years will be \(V(t)=P_0(1-r)^t\) for \(0\leq t\leq 5\). To the nearest dollar, find the value of a car \(4\) years after it is purchased for \(\$18,000\).