4.2-4.4 Solving Exponential Word Problems

Front

What is the formula for continuous compound interest?

Back

A = Pe^(rt), where A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), and t is the time the money is invested for in years.

Front

How do you calculate the interest rate when given the principal, amount after time, and time period for continuous compounding?

Back

Rearrange the formula A = Pe^(rt) to solve for r: r = (1/t) * ln(A/P).

Front

What does the variable 'a' represent in the exponential function y = ab^x?

Back

In the equation y = ab^x, 'a' represents the initial value or the y-intercept of the exponential function.

Front

How do you determine the total amount paid on a loan with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt) for loans with compound interest, where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the effect of increasing the compounding frequency on the total amount of interest earned?

Back

Increasing the compounding frequency results in more interest being earned, as interest is calculated and added to the principal more frequently.

Front

What is the growth rate of a population modeled by continuous exponential growth?

Back

The growth rate is expressed as a percentage and is used in the formula P(t) = P0 * e^(rt), where P0 is the initial population, r is the growth rate, and t is time.

Front

How do you calculate the future population of a growing bacteria culture using continuous growth?

Back

Use the formula P(t) = P0 * e^(rt), where P0 is the current population, r is the growth rate, and t is the time in the same units as the growth rate.

Front

What is the difference between simple interest and compound interest?

Back

Simple interest is calculated only on the principal amount, while compound interest is calculated on the principal and also on the accumulated interest from previous periods.

Front

How do you find the value of 'b' in the exponential function y = ab^x when given two points?

Back

Use the two points to create a system of equations and solve for 'b' by dividing the equations to eliminate 'a'.

Front

What is the formula for calculating the total amount paid on a loan with interest compounded quarterly?

Back

A = P(1 + r/4)^(4t), where A is the total amount, P is the principal, r is the annual interest rate, and t is the number of years.