Question

Lucy's lemonade stand has increasing profits each week during the hot summer months . Lucy finds that each week during the summer her profits increase by 10% over what they were the previous week in her first week of business, her profits were $50 How much money will she make in all over 4 weeks? Enter your answer rounded to the nearest cent, in the box

Answer 1

Answer:

She will make $232.1 in all over 4 weeks.

Step-by-step explanation:

Lucy's lemonade stand has increasing profit each week = 10%

Her profit for the initial week = $50.00

here the profit earned in every week will make a geometrical sequence.

In this sequence first term (a) = $50

and the common ratio (r) =  $(1+\frac{10}{100})$ = 1.1

sum of n terms of this sequence = $\frac{a(r^n-1)}{r-1}$

by substituting the values,

$=\frac{50[(1.1)^4-1]}{1.1-1}$

$=\frac{50(1.4641-1)}{0.1}$

$=\frac{50(0.4641)}{0.1}$

$=\frac{23.205}{0.1}$

= 232.05 ≈ $232.1

She will make $232.1 in all over 4 weeks.