Emily’s dad pays her for picking strawberries. Each hour she works he increases her pay. The first hour she earns two cents, the second hour she earns four cents, the third hour eight cents, and so on, doubling the amount each hour. How much money will she earn if she works six hours? How much money will she earn after ten hours? How many hours will she need to work to earn at least $5.00?

Hour 1: 0.02

Hour 2: 0.04
Hour 3: 0.08
Hour 4: 0.16
Hour 5: 0.32
Hour 6: 0.64

Add these 6 numbers together to find your first hour.

Keep doubling the preceding number to find the other two answers.

what do u mean by add your six numbers to get your first hour.

Sorry -- it should add those numbers to find your first ANSWER.

thanks i figured it out

your numbers form a geometric sequence where

a = .02
r = 2

Term(6) = ar^5 = .02(2^5) = .02(32) = .64
term(10) = ar^9 = .02(2^9) = .02(512) = 10.24

ar^(n-1) > 5.00
.02(2)^(n-1) > 5
2^(n-1) > 250

I know 2^7 = 128 and 2^8 = 256

so what do you think?

$5.10, calculated as follows:

$.02 + $.04 = $.06 + $.08 = $.14 +$.16 = $.30 + $.32 = $.62 + %,64 = $1.26 + $1.28 = $2.54 + $.56 = $.10

To find out how much money Emily will earn after working a certain number of hours, we need to observe the pattern of her increasing pay.

Let's break down the problem step by step:

1. How much money will Emily earn if she works 6 hours?
To determine her earnings, we need to calculate the pay for each hour and then sum them up.

Hour 1: $0.02
Hour 2: $0.04
Hour 3: $0.08
Hour 4: $0.16
Hour 5: $0.32
Hour 6: $0.64

By adding up these amounts, we find that Emily will earn a total of $1.26 if she works for 6 hours.

2. How much money will Emily earn after 10 hours?
Following the same pattern, we calculate her earnings:

Hour 7: $1.28
Hour 8: $2.56
Hour 9: $5.12
Hour 10: $10.24

Summing up these amounts, Emily will earn a total of $20.50 after working for 10 hours.

3. How many hours will Emily need to work to earn at least $5.00?
We start by calculating her earnings for each hour until we reach or exceed $5.00.

Hour 1: $0.02
Hour 2: $0.04
Hour 3: $0.08
Hour 4: $0.16
Hour 5: $0.32
Hour 6: $0.64
Hour 7: $1.28
Hour 8: $2.56
Hour 9: $5.12

Emily will reach her goal of earning at least $5.00 after working for 9 hours.

In summary:
- Emily will earn $1.26 if she works for 6 hours.
- Emily will earn $20.50 if she works for 10 hours.
- Emily will need to work for 9 hours to earn at least $5.00.