Question

Total personal income of the country (in billions of dollars) for selected years from 1960 to 2005 is given in the table.(a) These data can be modeled by an exponential function. Write the equation of this function, with x as the number of years after 1960.(b) If this model is accurate, what will be the country's total personal income in 2010?(c) In what year does the model predict the total personal income will reach $21 trillion?

Answer 1

Part a

using an exponential regression calculator

we have the ordered pairs

(0,409.8)

(10,837.1)

(20,2,307.4)

(30,4,880.9)

(40,8,428.7)

(45,10,231.2)

Please wait a minute to calculate the regression

we have that

y=443.86*(1.076)^x

Part b

the year 2010

t=2010-1960=50 years

substitute in the equation

y=443.86*(1.076)^50

y=17,293 billion of dollars

Part c

Remember that

One trillion dollars is equivalent to a thousand billion

so

1 trillion dollars=1,000 billion dollars

21 trillion dollars=21,000 billion dollars

For y=21,000

substitute in the equation

21,000=443.86*(1.076)^x

solve for x

21,000/443.86=1.076^x

apply log on both sides

x=log[21,000/443.86]/log(1.076)

x=52.65 years -------> 53 years

therefore

the year is 1960+53=2013