(2,3) is your answer for the equation
The answer is <span>$103.
To determine </span><span> how much Eileen will spend on gasoline, first we need to calculate how many gallons she needs.
If she drives 850 miles and </span><span>her car gets 23 miles per gallon, we can use the proportion:
850 miles : x gallons = 23 miles : 1 gallon
Crossing the products:
x = 850 miles </span>× 1 gallon ÷ 23 miles
x = 36.96 gallons
Thus, Eileen needs 36.96 gallons of gas. If the cost per gallon of gas is$2.79, using the proportion:
36.96 gallons : x = 1 gallon : <span>$2.79
x = 36.96 gallons </span>× $2.79 <span>÷ 1 gallon
x = </span>$103.12
x ≈ $<span>103</span>
T = 5, so after 5 years
p(t) = t^3 - 14t^2 + 20t + 120
Take derivative to find minimum:
p’(t) = 3t^2 - 28t + 10
Factor to solve for t:
p’(t) = (3t - 2)(t - 5)
0 = (3t - 2)(t - 5)
0 = 3t - 2
2 = 3t
2/3 = t
Plug 2/3 into original equation, this is a maximum. We want the minimum:
0 = t - 5
5 = t
Plug back into original:
5^3 - 14(5)^2 + 20(5) + 120
125 - 14(25) + 100 + 120
125 - 350 + 220
- 225 + 220
p(5) = -5
