Mary's parents decided to give her an allowance every Saturday. The first Saturday they gave her $.01. For each successive week, they double the amount given the previous week. If Mary saves her allowance, in how many weeks will she be a millionare?
I'm not sure what the answer is, but I think I might know how you will be able to figure it out. Take the $.01 Mary got the first week and double it to get what she got the second week ($.02). Then multiply the $.02 by 2 to get what she got the third week ($.04) Progress- ivly do that until you get $1,000,000.
THis question is from the Abeka 7th grade math book p. 175 #17.
27 weeks.
28 weeks
28 weeks
the answer is 27 weeks but doing it the way that Emily does it gets me to 26 weeks. I still dont understand
To calculate the number of weeks it will take for Mary to become a millionaire, we need to find out when the total amount of money she receives reaches or exceeds $1,000,000.
Let's break down the problem step by step:
1. On the first Saturday, Mary receives $0.01.
2. On the second Saturday, she receives double the amount of the previous week, so she gets $0.01 * 2 = $0.02.
3. On the third Saturday, she again receives double the amount of the previous week, so she gets $0.02 * 2 = $0.04.
4. This pattern continues, with each successive week doubling the amount of the previous week.
To find the total amount of money Mary receives in a given week, we can use the formula:
Total Amount = Initial Amount * (2 ^ (Week - 1))
Where:
- Initial Amount = $0.01 (as given in the problem)
- Week = the week number we are calculating for
Let's set up an equation to find the number of weeks required for Mary to reach or exceed $1,000,000:
$1,000,000 ≤ $0.01 * (2^(Week - 1))
Now let's solve this equation:
$1,000,000 ≤ $0.01 * (2^(Week - 1))
Divide both sides by $0.01:
$1,000,000 / $0.01 ≤ 2^(Week - 1)
100,000,000 ≤ 2^(Week - 1)
To find the value of Week, we can take the logarithm of both sides of the equation. Since we're working with base 2, we can use the logarithm with base 2 (log2):
log2(100,000,000) ≤ log2(2^(Week - 1))
log2(100,000,000) ≤ Week - 1
log2(100,000,000) + 1 ≤ Week
Using a calculator, we find that log2(100,000,000) + 1 ≈ 26.575424759
So, Mary will become a millionaire in approximately 27 weeks.