Lesson 2: 6-2 Solving Exponential Equations and Inequalities

How is solving an exponential equation similar to solving a linear equation?
What must be true in order to use the Property of Equality for Exponential Equations?
If both sided of an exponential equation do not have the same base, can the equations be solved, explain.

exponential equation
compound interest
exponential inequality

A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
F.I.E.4 For exponential models, express as a logarithm the solution to ab^(ct)=d where a, c, and d are numbers and the base b is 2, 10, or e. Evaluate the logarithm using technology

see below

Simple exponential equations can be solved by rewriting one or both sides of the equation so that the bases are the same. Once that has been achieved, the Property of Equality for Exponential Functions can be used to solve for the variable.

Feral hogs are a highly adaptive species that causes significant ecological and economic damage. Suppose the population of feral hogs is growing exponentially and can be modeled by y=2.5(1.45)^x where x is the number of years since 2016 and y is the number of hogs in millions. You can use y=2.5(1.45)^x to determine how many hogs there will be in a given year or to determine the year in which the hog populations is at a certain level.

Remind students that (a^m)^n=a^(mn).

Allows students to develop their sense of consumerism by providing them with an initial deposit amount and having the shop around for the best interest rates. Students should record relevant information including bank name, account type, interest rate, how often interest is compounded, and restrictions on the account. Ask students to graph the growth of their initial deposit over time.

Use McGraw Hill resources

SAT link