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Question : Evaluate using a scientific or graphing calculator. Round the answer to three decimal places : 2151618

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Evaluate using a scientific or graphing calculator. Round the answer to three decimal places.

1) 4^{3.7}

A) 169.197

B) 168.897

C) 187.416

D) 14.800

2) 4^{-2.2}

A) 23.426

B) 0.047

C) 0.347

D) -8.800

3) 4√5

A) 512.000

B) 8.944

C) 22.195

D) 25.000

Solve for x using an equivalent exponential expression.

4) The rabbit population in a forest area grows at the rate of 8% monthly. If there are 240 rabbits in September, find how many rabbits (rounded to the nearest whole number) should be expected by next September. Use the function f(x) = 240(2.7)^{0.08t}.

A) 623 rabbits

B) 610 rabbits

C) 622 rabbits

D) 636 rabbits

5) A city has been growing at a rate of 0.8% annually. If there are currently 3,911,000 residents in the city, how many (to the nearest ten-thousand) would be living in this city six years from now? Use the function f(x) = 3,911,000(2.7)^{0.008t}.

A) 510,000

B) 4,130,000

C) 10,560,000

D) 4,100,000

6) The function f(x) = 300(0.5)^{x/50} models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. Find the amount of radioactive material in the vault after 60 years. Round to the nearest whole number.

A) 131 pounds

B) 125 pounds

C) 180 pounds

D) 168 pounds

7) The formula S = A(((1 + r)^{t + 1} - 1/r)) models the value of a retirement account, where A = the number of dollars added to the retirement account each year, r = the annual interest rate, and S = the value of the retirement account after t years. If the interest rate is 11%, how much will the account be worth after 40 years if $1,000 is added each year? Round to the nearest whole number.

A) $72,142

B) $2,665,036

C) $41,000

D) $646,827

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

8) Using the formula A = P(1 + (r/n)^{nt}, find the interest on an investment of $1200, at an interest rate of 12% for 5 years, if the interest is compounded quarterly.

9) The formula for finding the monthly payment for an amortized loan is:

M = P[(R/1- (1 + R)^{-N}], where M is the monthly payment, R is the interest rate PER MONTH, and N is the number of months. Find the monthly payment on a home loan of $100,000 at 6% for 30 years.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

10) Use the compound amount formula A = P(1 + (r/n)^{nt }to find the accumulated amount on an investment of $1,500 invested at an interest rate of 10% for 18 months, if the interest is compounded weekly.

A) $9,058.80

B) $1,552.78

C) $1,742.50

D) $1,795.52

11) Use the compound amount formula A = P(1 + (r/n)^{nt }to find the accumulated amount on an investment of $250 invested at an interest rate of 6% for 5 years, if the interest is compounded monthly.

A) $8,246.92

B) $337.21

C) $334.56

D) $1,325.00

12) Brian invested $4000 at an interest rate of 5% for 10 years, where the interest was compounded semiannually. If A = P(1 + (r/n)^{nt }calculate the accumulated amount.

A) $6,554.47

B) $26,217.88

C) $3,277.24

D) $13,108.94

13) Tracy invested $6000 at an interest rate of 3% for 2 years, where the interest was compounded semi-annually. If A = P(1 + (r/n)^{nt }calculate the accumulated amount.

A) $636.82

B) $12,736.36

C) $25,472.73

D) $6,368.18

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

14) The formula for finding the monthly payment for an amortized loan is:

M = P[(R/1- (1 + R)^{-N}], where M is the monthly payment, R is the interest rate PER MONTH, and N is the number of months. Find the monthly payment on a car loan of $20,000 at 12% for 5 years.

15) The formula for finding the monthly payment for an amortized loan is:

M = P[(R/1- (1 + R)^{-N}], where M is the monthly payment, R is the interest rate PER MONTH, and N is the number of months. Find the monthly payment on a car loan of $10,000 at 9% for 3 years.

16) The formula for finding compound interest is A = P(1 + (r/n)^{nt} where A is the accumulated amount, P is the principal invested, r is the rate of interest, t is the time in years, and n is the number of compounds each year. Find the accumulated amount if the principal invested is $5,000, the rate is 8%, the compounds each year is 4 (quarterly), and the number of years is 5.

17) The formula for finding compound interest is A = P(1 + (r/n)^{nt} where A is the accumulated amount, P is the principal invested, r is the rate of interest, t is the time in years, and n is the number of compounds each year. Find the accumulated amount if the principal invested is $10,000, the rate is 12%, the compounds each year is 12 (monthly), and the number of years is 6.

18) The formula for finding compound interest is A = P(1 + (r/n)^{nt} where A is the accumulated amount, P is the principal invested, r is the rate of interest, t is the time in years, and n is the number of compounds each year. Find the accumulated amount if the principal invested is $8,000, the rate is 6%, the compounds each year is 2 (semi-annually), and the number of years is 12.