Disposable income is the amount available for spending and saving after taxes have been paid and is one gauge for the state of the economy. Using U.S. Energy Administration data for selected years from 2010 and projected to 2040, the total U.S. disposable income, in billions, can be modeled byD(t) = 10,020e0.02292twhere t is the number of years past 2010. In what year is disposable income predicted to be $17 trillion (that is, $17,000 billion)?

Question
Asked Oct 29, 2019
3 views
Disposable income is the amount available for spending and saving after taxes have been paid and is one gauge for the state of the economy. Using U.S. Energy Administration data for selected years from 2010 and projected to 2040, the total U.S. disposable income, in billions, can be modeled by
D(t) = 10,020e0.02292t
where t is the number of years past 2010. In what year is disposable income predicted to be $17 trillion (that is, $17,000 billion)?
check_circle

Expert Answer

Step 1
The total U.S. disposable income, in billions can be modeled by
D(t) 10,020e
0.02292t
Where t is the number of years past 2010.
help_outline

Image Transcriptionclose

The total U.S. disposable income, in billions can be modeled by D(t) 10,020e 0.02292t Where t is the number of years past 2010.

fullscreen
Step 2

Find the year in which the predicted disposable ...

17,000 10,020e.02292
1.6966 =0.02292
In(1.6966) 0.022921
0.52863
t =
0.02292
t 23.06
t 23
help_outline

Image Transcriptionclose

17,000 10,020e.02292 1.6966 =0.02292 In(1.6966) 0.022921 0.52863 t = 0.02292 t 23.06 t 23

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Algebra