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 (in million dollars) from licenses in 1990?
b. Write an equation that gives the revenue (in million dollars) as a function of the
number of years since 1990.
c. Find the revenue from licenses in 1999.

you have an AP with

d = 499.79
a_11 = 15099
a+10*499.79 = 15099
So a_n = 10101.1 + 499.79n

a. Well, if the revenue increased at a rate of 499.79 million dollars per year from 1990 to 2000, and in 2000 it was 15,099 million dollars, then we can go back in time and calculate approximately how much it was in 1990. Let's just say they were having a big party in 1990 because the revenue from licenses was around 1,000 million dollars. Woo!

b. Let's use our super mathematical powers and come up with an equation! If we let x represent the number of years since 1990 and y represent the revenue in million dollars, then our equation would be something like this: y = 499.79x + 1000. Easy peasy lemon squeezy!

c. Ah, 1999, the year before 2000. To find out the revenue from licenses in that year, all we have to do is substitute x = 9 into our equation from part b. So, y = 499.79(9) + 1000. Get your calculators ready! The revenue from licenses in 1999 was approximately 5,497.11 million dollars.

a. To find the approximate revenue from licenses in 1990, we need to determine the increase in revenue per year from 1990 to 2000 and then subtract that amount from the revenue in 2000.

Increase in revenue per year: 499.79 million dollars
Revenue in 2000: 15,099 million dollars

To find the approximate revenue from licenses in 1990:
1990 revenue = 2000 revenue - (increase in revenue per year * number of years)

1990 revenue = 15,099 million dollars - (499.79 million dollars/year * 10 years)
1990 revenue = 15,099 million dollars - 4,997.9 million dollars
1990 revenue = 10,101.1 million dollars

Therefore, the approximate revenue from licenses in 1990 was 10,101.1 million dollars.

b. The equation that gives the revenue as a function of the number of years since 1990 is:
Revenue (in million dollars) = (increase in revenue per year * number of years) + 1990 revenue

Revenue (in million dollars) = (499.79 million dollars/year * (number of years since 1990)) + 10,101.1 million dollars

c. To find the revenue from licenses in 1999, we substitute the number of years since 1990 as 9 into the equation derived in part (b):

Revenue in 1999 = (499.79 million dollars/year * 9 years) + 10,101.1 million dollars
Revenue in 1999 = 4,497.11 million dollars + 10,101.1 million dollars
Revenue in 1999 = 14,598.21 million dollars

Therefore, the revenue from licenses in 1999 was approximately 14,598.21 million dollars.

a. To find the approximate revenue from licenses in 1990, we can use the given information that the revenue increased at a constant rate of 499.79 million dollars per year. We need to find the number of years from 1990 to 2000 and determine the revenue increase over that period.

Number of years from 1990 to 2000 = 2000 - 1990 = 10 years

Total increase in revenue over 10 years = 499.79 million dollars/year * 10 years = 4997.9 million dollars

Revenue in 2000 = 15,099 million dollars

Revenue in 1990 ≈ Revenue in 2000 - Total increase in revenue
Revenue in 1990 ≈ 15,099 million dollars - 4997.9 million dollars
Revenue in 1990 ≈ 9,101.1 million dollars

Therefore, the approximate revenue from licenses in 1990 was 9,101.1 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 concept of linear equations.

Let's define the number of years since 1990 as x, and the revenue as y.

The given constant rate of increase is 499.79 million dollars per year.

Using the point-slope form of a linear equation, we can write:

y - y₁ = m(x - x₁)

Where:
y₁ = revenue in 1990 = 9,101.1 million dollars
x₁ = number of years since 1990 = 0
m = constant rate of increase = 499.79 million dollars per year

Plugging in the values, we get:

y - 9,101.1 = 499.79(x - 0)
y - 9,101.1 = 499.79x
y = 499.79x + 9,101.1

Therefore, the equation that gives the revenue as a function of the number of years since 1990 is y = 499.79x + 9,101.1.

c. To find the revenue from licenses in 1999, we need to substitute the number of years since 1990 (x = 9) into the equation from part b.

Revenue in 1999 (y) = 499.79x + 9,101.1
Revenue in 1999 (y) ≈ 499.79 * 9 + 9,101.1
Revenue in 1999 (y) ≈ 4497.11 + 9,101.1
Revenue in 1999 (y) ≈ 13,598.21 million dollars

Therefore, the revenue from licenses in 1999 was approximately 13,598.21 million dollars.