A package of modeling clay was shaped like a cone with a radius of 24 cm and a height of 6 cm. Miriam used all the clay to make
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Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:
Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:
Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
The amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)
<h3>How to calculate compound interest's amount?</h3>If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
The final amount becomes:
For the considered case, we're given that:
- Initial amount Laura deposited = $5,500 = P
- Type of interest: Compound interest
- Unit of time: Annually
- Rate of interest = 1.6% annually = R
- Total unit of time for which amount is to be calculated: 4 years = T
The final amount at the end of 4 years in the considered account of Laura is evaluated as:
Thus, he amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)
Learn more about compound interest here: