Answer:
The first graph.
Step-by-step explanation:
An exponential function has a graph that is a smooth curve; it either increases at an ever increasing rate or decreases at an ever increasing rate.
The only graph that fits these characteristics is the first one.
The answer is the second choice: 24 gallons of gasoline
Solve for x: by completing the square:
x^3 + 7 x^2 - 12 x - 18 = 0
The left hand side factors into a product with two terms:
(x + 1) (x^2 + 6 x - 18) = 0
Split into two equations:
x + 1 = 0 or x^2 + 6 x - 18 = 0
Subtract 1 from both sides:
x = -1 or x^2 + 6 x - 18 = 0
Add 18 to both sides:
x = -1 or x^2 + 6 x = 18
Add 9 to both sides:
x = -1 or x^2 + 6 x + 9 = 27
Write the left hand side as a square:
x = -1 or (x + 3)^2 = 27
Take the square root of both sides:
x = -1 or x + 3 = 3 sqrt(3) or x + 3 = -3 sqrt(3)
Subtract 3 from both sides:
x = -1 or x = 3 sqrt(3) - 3 or x + 3 = -3 sqrt(3)
Subtract 3 from both sides:
Answer: x = -1 or x = 3 sqrt(3) - 3 or x = -3 - 3 sqrt(3)
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