Exercise 59 Page 280

In exponential functions of the form y=a(b)^x, a is the y-intercept.

f(7)=- 192

Practice makes perfect

We will start by writing an exponential function representing the graph. We know that any exponential function has the form below. y= a( b)^x Here, a is the y-intercept and b is the constant multiplier.

We see that - 1.5 is the y-intercept, so a= - 1.5. y= a(b)^x ⇔ y= - 1.5(b)^x The point ( 1, - 3) is on the curve. Using this point, we can find b.

y=- 1.5(b)^x

SubstituteII

x= 1, y= - 3

- 3=- 1.5(b)^1

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Solve for b

ExponentOne

a^1=a

- 3=- 1.5(b)

DivEqn

.LHS /(- 1.5).=.RHS /(- 1.5).

- 3/- 1.5=b

CalcQuot

Calculate quotient

2=b

RearrangeEqn

Rearrange equation

b=2

The constant multiplier of the function is 2. y=- 1.5( b)^x ⇔ y=- 1.5( 2)^x The given graph represents the function f(x)=- 1.5 (2)^x. Let's find f(7).

f(x)=- 1.5 (2)^x

Substitute

x= 7

f( 7)=- 1.5 (2)^7

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Simplify right-hand side

CalcPow

Calculate power

f(7)=- 1.5(128)

Multiply

f(7)=- 192

The function is equal to - 192 when x=7.