Unit 1: Relationships between Quantities and Reasoning with Equations
Lesson 13 Writing Exponential Equations in Two Variables
Objectives:

I can write an exponential equation with two variables to model a situation, solve it, and graph it.

I can determine if a model is an example of exponential growth or exponential decay.
WarmUp: Review.
Solve.
a) 42^{x} + 1 = 17
b) 3^{x} + 19 = 100

Graph.
Is it linear?

Exponential Equations:
An exponential equation is an equation in which the independent variable is an exponent. In the exponential equation y = ab^{x}, y is the dependent variable, x, is the independent variable, and a and b are constants. The base, b, can be any positive real number other than 1.
Is it exponential?
y = 3^{2x} Why or why not?

y = 7x^{3} Why or why not?

In y = ab^{x}, the constant a represents the starting value of a quantity being measured, such as the number of living things in an area. The base b shows how that quantity changes as the variable x changes.
The graph of an exponential equation is not a straight line. It is a curve that is either always increasing or always decreasing.
Exponential Growth Graph
For the equation y = ab^{x}, b > 1 and a > 0.

Exponential Decay Graph
For the equation y = ab^{x}, 0 < b < 1 and a > 0.

Is it exponential growth, exponential decay, or neither?
y = 2^{x}

y = 3 0.5^{x}

y =

y = 54^{x}

y =

y =

Graphing Exponential Equations:
We will need to make an input output table to graph exponential equations.
Graph.
We can use the information we have learned about exponentials to write an equation that models an exponential growth or exponential decay problem.
Let’s try a few…
You try! Exit Ticket.
A population of rabbits quadruples each year. If the population started out with 24 rabbits, write an equation that represents the total population after x years. Then, graph the equation.
How many rabbits would there be after 4 years if none of the rabbits died?

Name: _________________________
Unit 1 Lesson 13: Writing Exponential Equations with Two Variables
Write an equation for each situation.
1) Sarah bought a car for $18,500. According to her insurance company, the value of the car depreciates 5% each year. What will the value of the car be x years after Sarah purchased it?

2) A colony of bacteria doubles in population every 24 hours. If there were 20 bacteria initally, how many bacteria will there be after x days?

3) Caitlin put $300 in a bank account with 4% annual interest compounded monthly. Write an equation to represent the total amount of money in Caitlin’s account after t months.

Write the equation that models the situation and then graph the equation.
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