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.
To answer these questions, we can use the given information about the constant rate of increase and the revenue in 2000. Let's break down each question:
a) What was the approximate revenue from licenses in 1990?
Since we know that the revenue increased at a constant rate of 499.79 million dollars per year from 1990 to 2000, we can calculate the increase by multiplying the rate by the number of years: 499.79 million/year * 10 years = 4,997.9 million dollars.
To find the revenue in 1990, we subtract the increase from the revenue in 2000: 15,099 million dollars - 4,997.9 million dollars = 10,101.1 million dollars.
Therefore, the approximate revenue from licenses in 1990 was approximately 10,101.1 million dollars.
b) Write an equation that gives the revenue as a function of the number of years since 1990.
Let's call the revenue R and the number of years since 1990 as Y.
Since the revenue increases at a constant rate of 499.79 million dollars per year, we can write the equation as:
R = 499.79Y + R₀,
where R₀ represents the revenue in the starting year, in this case, 1990.
c) Find the revenue from licenses in 1999.
To find the revenue from licenses in 1999, we need to substitute Y = 9 (since 1999 is 9 years after 1990) into the equation from part b:
R = 499.79(9) + R₀,
R = 4,497.11 + R₀.
Given that the revenue in 2000 was 15,099 million dollars, we can substitute R = 15,099 million dollars into the above equation and solve for R₀:
15,099 million dollars = 4,497.11 million dollars + R₀,
R₀ ≈ 10,601.89 million dollars.
Therefore, the revenue from licenses in 1999 was approximately 10,601.89 million dollars.
a. y = mx + b
15099 = 499.79(10) + b
b = 10101.1
y = 499.79x + 10101.1
b. y = 499.97x + 10101.1
y = 499.79(0) + 10101. 1
y = $10101.1
c. y = 499.79x + 10101.1
y = 499.79(9) + 10101.1
y = $14599.21