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Pearson Algebra 2 Common Core, 2011
PA
Pearson Algebra 2 Common Core, 2011 View details
End-of-Course Assessment

Exercise 40 Page 968

Any exponential function can be written as f(x)=ab^x.

A

Practice makes perfect

We are given a table that represents an exponential function.

x f(x)
- 2 12
-1 6
0 3
1 1.5

We want to write an appropriate equation for this data. To do so, let's recall the form for an exponential function. f(x)=ab^xTo find the values of a and b, we will use two of the ordered pairs given in the table. For simplicity, we will use ( 0, 3) and ( - 1, 6). Let's start by substituting 0 for x and 3 for f(x).

f(x)=ab^x
SubstituteII

x= 0, f(x)= 3

3=ab^0
â–¼
Solve for a
ExponentZero

a^0=1

3=a(1)
IdPropMult

Identity Property of Multiplication

3=a
RearrangeEqn

Rearrange equation

a=3

Now that we know that a= 3, we can partially write the equation. f(x)= 3b^x To find the value of b, we will substitute - 1 for x and 6 for f(x) in the above equation.

f(x)=3b^x
SubstituteII

x= - 1, f(x)= 6

6=3b^(- 1)
â–¼
Solve for b
NegOneExponentToFrac

a^(- 1)=1/a

6=3/b
MultEqn

LHS * b=RHS* b

6b=3
DivEqn

.LHS /6.=.RHS /6.

b= 3/6
ReduceFrac

a/b=.a /3./.b /3.

b= 1/2

Now that we know that a= 3 and b= 12, we can write the full equation that models the data in the given table.

f(x) = ab^x
SubstituteII

a= 3, b= 1/2

f(x) = 3 ( 1/2)^x
PowQuot

(a/b)^m=a^m/b^m

f(x)=3 (1^x/2^x )
BaseOne

1^a=1

f(x)=3 (1/2^x )
FracToNegExponent

1/a^m=a^(- m)

f(x) = 3(2^(- x))

This corresponds to option A.

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arrow_right Exercises p.964-971
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Exercises 3 (Page 964)
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