Algebra 2 help!

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

Since Lucy's profit the first week was $50 which represented 10% of her initial investment of $500 (50/0.1=500).

The compound interest formula is T = P(1+i)^t, where T = total at time t, P = initial investment (here $500), i = rate of increase (here 10% or 0.1) and t = time (in weeks).

At time 1 week, the total T = 500(1+0.1)¹ = 500(1.01) = $550, which confirms Lucy's total at 1 week including profit.

At time 4 weeks, the Total T = 500(1+0.1)⁴ = 500(1.4641) = $732.05. Therefore, Lucy's total profit after 4 weeks = $732.05 - $500 = $232.05.

Answer 2

Let us do it this way instead of using a formula for compound interest

First week ,10% gain = $50

So initial investment is $500 Which becomes $550 at the end of first week

P1 = $50

New investment =$550

10% 0f it = 0.1*550 = $55

P2 = $55

New Investment= $605 ( 550 +55)

10% of it = $60.50

P3 = $60.50

New Investment = 605+60.50 = 665.50

10% of it = $66.55

P4 = $66.55

Now add P1 , P2 , P3 and P4