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QuestionHow many years after 2014 will the average price of new cars reach \$ 43,850 if it increases by \$ 1,250 per year?

Studdy Solution

STEP 1

Assumptions1. The average price of a new car in2014 is \$37,600. The price of new cars increases by approximately \$1250 per year3. We want to find out when the average price of a new car will be \$43,850

STEP 2

First, we need to find out how much the price of a new car needs to increase to reach \$43,850. We can do this by subtracting the initial price from the target price.
Price increase=Target price−Initial pricePrice\, increase = Target\, price - Initial\, price

STEP 3

Now, plug in the given values for the target price and initial price to calculate the price increase.
Price increase=$43,850−$37,600Price\, increase = \$43,850 - \$37,600

STEP 4

Calculate the price increase.
Price increase=$43,850−$37,600=$6,250Price\, increase = \$43,850 - \$37,600 = \$6,250

STEP 5

Now that we have the price increase, we can find out how many years it will take for the price of a new car to increase by this amount. We can do this by dividing the price increase by the annual increase in price.
Years=Price increase/Annual increaseYears = Price\, increase / Annual\, increase

STEP 6

Plug in the values for the price increase and the annual increase to calculate the number of years.
Years=$6,250/$1,250Years = \$6,250 / \$1,250

STEP 7

Calculate the number of years.
Years=$6,250/$1,250=5Years = \$6,250 / \$1,250 =5So, it will take5 years after2014 for the average price of a new car to reach \$43,850.

STEP 8

To find out in which year this will occur, we can add the number of years to the initial year.
Year=Initial year+YearsYear = Initial\, year + Years

STEP 9

Plug in the values for the initial year and the number of years to calculate the year.
Year=2014+5Year =2014 +5

STEP 10

Calculate the year.
Year=2014+5=2019Year =2014 +5 =2019So, the average price of a new car will reach \$43,850 in the year2019.

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