32 select the correct answer. jessica opened an apparel shop five years ago. in the first year, she made a…

32 select the correct answer. jessica opened an apparel shop five years ago. in the first year, she made a profit of $3,125. each year after that, her profit was 20 percent more than in the previous year. what is the total profit jessica earned in 5 years? a. $32,400 b. $23,255 c. $7,776 d. $6,480

32 select the correct answer. jessica opened an apparel shop five years ago. in the first year, she made a profit of $3,125. each year after that, her profit was 20 percent more than in the previous year. what is the total profit jessica earned in 5 years? a. $32,400 b. $23,255 c. $7,776 d. $6,480

Answer

Explanation:

Step1: Identify the first - year profit and growth rate

The first - year profit $a_1 = 3125$, and the growth rate $r=1 + 0.2=1.2$.

Step2: Use the sum formula for a geometric series

The sum of a geometric series $S_n=\frac{a_1(1 - r^n)}{1 - r}$ for $r\neq1$, where $n = 5$. Substitute $a_1 = 3125$, $r = 1.2$, and $n = 5$ into the formula: [ \begin{align*} S_5&=\frac{3125\times(1 - 1.2^5)}{1 - 1.2}\ &=\frac{3125\times(1 - 2.48832)}{- 0.2}\ &=\frac{3125\times(-1.48832)}{-0.2}\ &=\frac{-4651}{-0.2}\ &=23255 \end{align*} ]

Answer:

B. $$23,255$