Question

The hourly wage of some Toyota automobile assembly line workers is being increased annually by the same percentageIf their wage went from $6.60 to $15.70 in 15 years what is the doubling time?____(nearest year)

Answer 1

we have that

$6.60 -----> represents 100%

Find out the difference

($15.70-$6.60)=$9.10

Applying proportion

Find out how much percentage represents the difference

100/6.60=x/9.10

solve for x

x=(100/6.60)*9.10

x=137.88%

Divide by 15

137.88%/15=9.19% each year

we have the exponential growth equation of the form

y=a(b)^x

where

a=6.60

b=1+0.0919=1.0919

x ----> number of years

y ----> hourly wage

so

For y=2(6.60)=$13.20

substitute in the equation

13.20=6.60(1.0919)^x

solve for x

(13.20/6.60)=(1.0919)^x

2=(1.0919)^x

apply log both sides

log(2)=x*log(1.0919)

x=7.9 years

x=8 years

the answer is 8 years