CPM Homework Help : CCAA8 Problem 6-76

During a two-month period gasoline increased from $$4.10$ per gallon to $$4.35$ per gallon. Assuming prices increased in a geometric sequence, what was the monthly multiplier and what was the percent increase?

Hint:

To find the monthly multiplier, write an equation and solve for the variable.

New price = (original price)(multiplier for month 1)(multiplier for month 2)

Step 1:

$$4.35 = $4.10\left(x\right)\left(x\right) \text{ or } $4.35 = $4.10x^{2}$

Step 2:

$\frac{\$4.35}{\$4.10\ }=x^2$

Step 3:

$x=\sqrt{\frac{4.35}{4.10}}$

Answer:

$x ≈ 1.03$ Therefore the percent increase is $3\%$ .