Exam 16: Exponential and Logarithmic Equations

Use the compound amount formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the accumulated amount on an investment of $\$ 500$ , invested at an interest rate of $5 \%$ for 2 years, if the interest is compounded annually.

The compound amount when an investment is compounded continuously is A = Peni Where A = compound amount, P = original principal, n = # of years, and i = interest rate per year. Let P = 200, I = 0.06, and n = 4, then find A.

The formula for finding compound interest is $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ where A is the accumulated amount, P is the principal invested, r is the rate of interest, t is the time in years, and n is the number of compounds each year. Find the accumulated amount if the principal invested is $8,000, the rate is 6%, the compounds each year is 2 (semi-annually), and the number of years is 12.

The formula for finding the monthly payment for an amortized loan is: $M = P \left[ \frac { R } { 1 - ( 1 + R ) ^ { - N } } \right]$ , where $M$ is the monthly payment, $R$ is the interest rate PER MONTH, and $\mathrm { N }$ is the number of months. Find the monthly payment on a car loan of $\$ 20,000$ at $12 \%$ for 5 years.

Solve for x: $x : 8 ^ { x + 2 } = \frac { 1 } { 32 }$

Nancy invested $1800 at an interest rate of 6% for 4 years, where it was compounded continuously. If A = Peni, calculate the accumulated amount.

Tracy invested $\$ 6000$ at an interest rate of $3 \%$ for 2 years, where the interest was compounded semiannually. If $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ calculate the accumulated amount.

The formula for finding the amount an investment grows to if it is compounded continuously is A = Pert, A is the accumulated amount, P is the principal invested, e is the natural exponent, r is the rate per year, and t is the number of years. Find the accumulated amount A if $10,000 is compounded continuously for 3 years at 8% per year.

A suburb city presently has a population of 250,000 people. In 25 years, what would its estimated population be if P = Poe0.02t?

The formula A = Peni can also be used for exponential growth and decay applications. Use the formula to find the resulting amount from an original 52 g of a decomposing substance if it decomposes at a rate of 12% per century for 10 centuries.

Solve for $x : 2 ^ { 4 - x } = 64$

Use the compound amount formula $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the accumulated amount on an investment of $\$ 250$ invested at an interest rate of $6 \%$ for 5 years, if the interest is compounded monthly.

The formula for finding the monthly payment for an amortized loan is: $M = P \left[ \frac { R } { 1 - ( 1 + R ) ^ { - N } } \right]$ , where M is the monthly payment, R is the interest rate PER MONTH, and N is the number of months. Find the monthly payment on a car loan of $10,000 at 9% for 3 years.

Solve for x: $x : 4 x = \frac { 1 } { 64 }$

Solve for $x : 2 ^ { x } = 64$

Brian invested $\$ 4000$ at an interest rate of $5 \%$ for 10 years, where the interest was compounded semiannually. If $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ calculate the accumulated amount.

The compound amount when an investment is compounded continuously is A = Peni Where A = compound amount, P = original principal, n = number of years, and i = interest rate per year. Let P = 1000, I = 0.1, and n = 5, then find A.

Solve for $5 ^ { x } = \frac { 1 } { 25 }$