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QuestionJoe's income grows yearly. It was \$15,000 in year 1 and \$19,400 in year 5. When was it \$26,000?

Studdy Solution

STEP 1

Assumptions1. Joe's annual income increases each year by the same dollar amount. . The first year his income was 15,000.<br/>3.Thefifthyearhisincomewas15,000.<br />3. The fifth year his income was 19,400.
4. We need to find out in which year his income was $26,000.

STEP 2

First, we need to find out the annual increase in Joe's income. We can do this by subtracting the income of the first year from the income of the fifth year and then dividing by the number of years between the first and fifth year (which is4 years).
Annual increase=Income5th year−Income1st year5−1Annual\, increase = \frac{Income_{5th\, year} - Income_{1st\, year}}{5 -1}

STEP 3

Now, plug in the given values for the income of the first year and the fifth year to calculate the annual increase.
Annual increase=$19,400−$15,0005−1Annual\, increase = \frac{\$19,400 - \$15,000}{5 -1}

STEP 4

Calculate the annual increase in Joe's income.
Annual increase=$19,400−$15,000−1=$1,100Annual\, increase = \frac{\$19,400 - \$15,000}{ -1} = \$1,100

STEP 5

Now that we have the annual increase, we can find out in which year Joe's income was 26,000.Wecandothisbysubtractingtheincomeofthefirstyearfrom26,000. We can do this by subtracting the income of the first year from 26,000 and then dividing by the annual increase.
Year=1+$26,000−Income1st yearAnnual increaseYear =1 + \frac{\$26,000 - Income_{1st\, year}}{Annual\, increase}

STEP 6

Plug in the values for the income of the first year and the annual increase to calculate the year.
Year=1+$26,000−$15,000$1,100Year =1 + \frac{\$26,000 - \$15,000}{\$1,100}

STEP 7

Calculate the year in which Joe's income was $26,000.
Year=1+$26,000−$15,000$1,100=11Year =1 + \frac{\$26,000 - \$15,000}{\$1,100} =11Joe's income was $26,000 in the11th year.

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