PreCalc

1) Suppose you deposit $10,000 into an account earning 3.5% interest compounded quarterly. After n quarters the balance in the account is given by the formula: 0.035)” 10000 (1 + 4 )

a) Each quarter can be viewed as a term of a sequence. List the first 5 terms.

b) Identify the type of sequence this is. Explain.

c) Find the balance in the account after 30 quarters.

2) An object with negligible air resistance is dropped from the top of the Willis Tower in Chicago at a height of 1451 feet. During the first second of fall, the object falls 16 feet; during the second second, it falls 48 feet; during the third second, it falls 80 feet; during the fourth second, it falls 112 feet. Assuming this pattern continues, how many feet does the object fall in the first 7 seconds after it is dropped?

3) You borrow $5,000 from your parents to purchase a used car. The arrangements of the loan are such that you make payments of $250 per month toward the balance plus 1% interest on the unpaid balance from the previous month.

(a) Find the first year’s monthly payments and the unpaid balance after each month.

(b) Find the total amount of interest paid over the term of the loan.

4) A tool and die company buys a machine for $175,000 and it depreciates at a rate of 30% per year. (In other words, at the end of each year the depreciated value is 70% of what it was at the beginning of the year.) Find the depreciated value of the machine after 5 full years.

5) A ball is dropped from a height of 6 feet and begins bouncing. The height of each bounce is three-fourths the height of the previous bounce. Find the total vertical distance the ball travels before coming to rest.

 

 

 

 

 

 

 

Sample Solution

ACED ESSAYS