If your allowance was doubled everyday, how many days would it take for you to have over $1000(also tell how much you would have for that day added up?) How many days would it take for you to have over $10,000? (and how much for that day?)
depends on what the amount was at the start.
But, 2^10 = 1024
If your allowance was a penny doubled every day, how many days would it take for you to have over $1000.00? On which day would you have over $10000.00? How much money would you have on the 15th day?
If your allowance is doubled every day, we can calculate the amount you would have for each day using the formula:
Allowance for Day N = Allowance for Day N-1 * 2
Let's calculate the number of days it would take for you to have over $1,000:
Day 1: $1
Day 2: $1 * 2 = $2
Day 3: $2 * 2 = $4
Day 4: $4 * 2 = $8
Day 5: $8 * 2 = $16
Day 6: $16 * 2 = $32
Day 7: $32 * 2 = $64
Day 8: $64 * 2 = $128
For each day, the amount doubles. By day 8, you would have $128.
So, it would take 8 days to have over $1,000.
Now let's calculate the number of days it would take for you to have over $10,000:
Day 1: $1
Day 2: $1 * 2 = $2
Day 3: $2 * 2 = $4
Day 4: $4 * 2 = $8
Day 5: $8 * 2 = $16
Day 6: $16 * 2 = $32
Day 7: $32 * 2 = $64
Day 8: $64 * 2 = $128
Day 9: $128 * 2 = $256
Day 10: $256 * 2 = $512
Day 11: $512 * 2 = $1024
Day 12: $1024 * 2 = $2048
Day 13: $2048 * 2 = $4096
Day 14: $4096 * 2 = $8192
Day 15: $8192 * 2 = $16384
By day 15, you would have $16,384.
So, it would take 15 days to have over $10,000.
To find out how many days it would take to have over $1000 and over $10,000 if your allowance is doubled every day, we can use a simple mathematical approach.
Let's start with the calculation for having over $1000:
1. On the first day, assume your allowance is $1.
2. On the second day, your allowance will be doubled, so you will have $1 * 2 = $2.
3. On the third day, your allowance will double again, resulting in $2 * 2 = $4.
4. This doubling process continues each day. On the fourth day, you will have $4 * 2 = $8, and so on.
5. We can see the pattern; your allowance will be doubled each day. So, on day n, you will have an allowance of $2^n.
To find the number of days it takes to have over $1000, we need to solve the equation 2^n > 1000.
Taking the logarithm base 2 on both sides, we get:
log2(2^n) > log2(1000)
n * log2(2) > log2(1000)
n > log2(1000)
Using a calculator, we find that log2(1000) is approximately 9.97.
Therefore, it will take approximately 10 days to have over $1000. On the 10th day, you will have:
Allowance = $2^10 = $1024.
Now let's move on to calculating how many days it would take to have over $10,000.
To find the number of days it takes to have over $10,000, we solve the equation 2^n > 10000.
Using the same approach as before, we take the logarithm base 2 on both sides:
log2(2^n) > log2(10000)
n * log2(2) > log2(10000)
n > log2(10000)
Using a calculator, we find that log2(10000) is approximately 13.29.
Therefore, it will take approximately 14 days to have over $10,000. On the 14th day, you will have:
Allowance = $2^14 = $16,384.
So, after 10 days, you will have over $1000 (specifically $1024), and after 14 days, you will have over $10,000 (specifically $16,384).