Exponential Equations

Presentation

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Mathematics

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9th Grade

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Practice Problem

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Medium

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CCSS

HSF.LE.A.2, HSF-LE.A.1A, HSF.LE.B.5

Standards-aligned

Callie Warren

Used 38+ times

FREE Resource

8 Slides • 19 Questions

Writing Exponential Equations

What is an exponential equation?

a--initial value, y-intercept, never 0

b--growth or decay factor, never 0 or 1 (base)

x--exponent/power

Writing an equation

X-values should be a constant increase. Notice they increase by 1 each time. Y-values multiply by the same number each time.

To write equation, find the y-intercept (where x=0) and the rate of change for the y-values.
This table is, $f\left(x\right)=2^x$ ,since the y-int is 1 and it multiplies by 2.

Are these exponential?

A--Yes, multiplies by 3 each time
B--No, variable is not exponent
C--Yes, variable is exponent
D--No, adds 2, not mulitiply

What is this equation?

Y-values multiply by 3 each time, but there is not y-intercept listed. For x=0, you must divide 15/3 to "work backwards".

x=0 gives y=5

Equation:
$y=5\left(3\right)^x$

Multiple Choice

What is the equation for this table?

$f\left(x\right)=8\left(4\right)^x$

$f\left(x\right)=4^x$

$f\left(x\right)=2\left(4\right)^x$

Multiple Choice

What is the equation for this table?

$f\left(x\right)=\left(\frac{1}{2}\right)^x$

$f\left(x\right)=2^x$

$f\left(x\right)=\frac{1}{2}\left(1\right)^x$

Multiple Choice

Write the equation that represents the table below:

y=½(4)^x

y=2(4)^x

y=4(2)^x

y=4(½)^x

Multiple Choice

What is the pattern you see in this table?

Multiplying by 1/3

Subtracting 8

Multiplying by 3

Subtracting 3

Multiple Choice

Which of the equations below represent this table?

y=3⋅(36)^x

y=36⋅(3)^x

y=3⋅(⅓)^x

y=36⋅(⅓)^x

Finding the Equation from a Graph

1) Find the y-intercept----> (0, 1)
a=1

2) Find the next points--->(1, 2) (2, 4) (3,8) and look at how the y-values change. These x2 each time.
b=2

3) Write equation

f\left(x\right)=1\left(2\right)^x

What about this one?

Y-intercept is (0,2) ---> a=2
Look at other points->divided by 3 (same as x $\frac{1}{3}$ ) b=1/3
Equation is $f\left(x\right)=2\left(\frac{1}{3}\right)^x$

Multiple Choice

Which equation matches the graph?

y=2(2)^x

y=2(1/2)^x

y=2^x

y=1/2(2)^x

Multiple Choice

What is the equation that models this graph?

y = 2(3)^x

y = 3(2)^x

y = 3(½)^x

y =½(3)^x

Let's Do a Little Review!

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

y=5000(0.7)^x

y=30(5000)^x

y=5000(1.3)^x

y=5000x^x

Multiple Choice

What type of function is f(x)=2(1/7)^x ?

Exponential Growth

Linear

Exponential Decay

None of the Abovee

Multiple Choice

What is the growth for the function: f(x) = 800(0.85)^x?

800

0.85

0.15

Multiple Choice

Which the following graphs shows an exponential decay equation?

Multiple Choice

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

(.27)^x

.27

3.51

Multiple Choice

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What percent did the population increase each year?

It doesn't say

I don't know

400%

Multiple Choice

The amount of money in Carmen’s savings account is represented by the equation $A\left(t\right)=3500\left(1.025\right)^t$ where t represents years. How much will Carmen have in the account after 10 years?

$4,480.30

$4,480.29

$4,592.30

You can't tell from the equation.

Multiple Choice

The amount of money in Carmen’s savings account is represented by the equation $A\left(t\right)=3500\left(1.025\right)^t$ where t represents years. How much did Carmen originally deposit?

$1.025

$3,500

25%

1.025%

You can't tell from the equation.

Multiple Choice

The amount of money in Carmen’s savings account is represented by the equation $A\left(t\right)=3500\left(1.025\right)^t$ , where t represents years. What is the interest rate on the account (as a percent)?

.025%

.25%

2.5%

25%

Multiple Choice

1. The population of a school of fish decreases at a rate of 18% per month. There are currently 500 fish in the school. How many fish will there be in 3 months?

276

822

476

Multiple Choice

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

y=6(0.14)^x

y=6(1+14)^x

y=6(1.14)^x

y=6(0.86)^x

Multiple Choice

You bought a Boston Whaler in 2004 for $12,500. The boat's value depreciates by 7% a year. How much is the boat worth in 2012?

$11625

$6994.77

$21,477

$875

Writing Exponential Equations

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