The approximate percent P of average income used to pay federal, state, and local taxes is given by , where t is the number of years after 1950. The actual tax load for 1980 was 33.8%. What does the formula give as an approximation? Round your answer to one decimal place.
A) 18.6%
B) 42.1%
C) 33.4%
D) 13.8%
E) 42.9%

Question

The approximate percent P of average income used to pay federal, state, and local taxes is given by , where t is the number of years after 1950. The actual tax load for 1980 was 33.8%. What does the formula give as an approximation? Round your answer to one decimal place. 
A) 18.6% 
B) 42.1% 
C) 33.4% 
D) 13.8% 
E) 42.9%

Quizplus · Accepted Answer

The question tells us that the formula gives an approximation of the tax load as a percent of average income. We are given the actual tax load for 1980 as 33.8%, so we can set up an equation to solve for the value of k in the formula:

33.8 = k(1980-1950)

Simplifying:

33.8 = 30k
k = 1.126666...

So the formula is approximately:

P = 0.25 + 0.0011t + 1.1267

Plugging in t = 30 (since 1980 is 30 years after 1950):

P ≈ 33.4%

Therefore, the best choice is C, which matches the approximation given by the formula.

The Approximate Percent P of Average Income Used to Pay