the amount of revenue brought in by states from motor vehicle licenses increased at a relatively constant rate of 499.79 million dollars per year from 1990 to 2000. In 2000, the states brought in 15,099 million dollars in revenue from motor vehicle licenses.
a: what was the approximate revenue from licenses in 1990?
b: write an equation that gives the revenue as a function of the number of years since 1990.
c: find the revenue from licenses in 1999.
a: To find the approximate revenue from licenses in 1990, we can start with the revenue in 2000 and subtract the total increase over the ten-year period.
Revenue increase per year = 499.79 million dollars
Number of years from 1990 to 2000 = 2000 - 1990 = 10 years
Total increase over the ten-year period = Revenue increase per year * Number of years = 499.79 million dollars/year * 10 years = 4,997.9 million dollars
Revenue in 1990 = Revenue in 2000 - Total increase over the ten-year period = 15,099 million dollars - 4,997.9 million dollars = 10,101.1 million dollars
Therefore, the approximate revenue from licenses in 1990 was 10,101.1 million dollars.
b: To write an equation that gives the revenue as a function of the number of years since 1990, we can use the constant rate of increase.
Let R be the revenue in million dollars and t be the number of years since 1990.
We can write the equation as:
R = 499.79t + 10,101.1
c: To find the revenue from licenses in 1999, we can subtract 1 year from 2000 in the equation we derived in part b.
t = 1999 - 1990 = 9 years
Revenue in 1999 = 499.79 * 9 + 10,101.1
Revenue in 1999 ≈ 4,497.11 + 10,101.1 ≈ 14,598.21 million dollars
Therefore, the revenue from licenses in 1999 was approximately 14,598.21 million dollars.