Exercise 51 Page 280

Practice makes perfect

We want to write an exponential function representing the number y of visitors to an art gallery after x months. We know that any exponential function has the form below.

y= a( b)^xHere, a is the y-intercept and b is the constant multiplier.

We see that 40 is the y-intercept, so a= 40. y= a(b)^x ⇔ y= 40(b)^x The point ( 1, 60) is on the curve. Using this point we can find b.

y=40(b)^x

SubstituteII

x= 1, y= 60

60=40(b)^1

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Solve for b

ExponentOne

a^1=a

60=40(b)

DivEqn

.LHS /40.=.RHS /40.

60/40=b

CalcQuot

Calculate quotient

1.5=b

RearrangeEqn

Rearrange equation

b=1.5

The constant multiplier of the function is 1.5. y=40( b)^x ⇔ y=40( 1.5)^x This function represents the situation.

To find the number of visitors after 5 months, we will substitute 5 for x.

y=40(1.5)^x

Substitute

x= 5

y=40(1.5)^5

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Simplify right-hand side

CalcPow

Calculate power

y=40(7.59375)

Multiply

y=303.75

RoundInt

Round to nearest integer

y=304

The approximate number of visitors after 5 months will be 304.

Subchapter links

Communicate Your Answer p.273

Monitoring Progress p.274-277

Exercises p.278-280

Exercise 51 Page 280

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