Business Math Exam 2 Review

Exponents

100

f(x) = 2^x, what is f(4)?

f(4)=16

200

graph 3^(x+5).

https://www.desmos.com/calculator/1uh0lxbaaz

300

If f(x) = a^x, and f(2)=25, find f(3).

f(3)=125

400

e^3.3673=29. Convert to a logarithmic statement.

ln29= 3.3673

500

4^6x-3=256. Solve this exponential equation without logarithms.

x= 7/6 or 1.16

Exponentials pt. 2 (worth +100)

100

5^x=14. 

Solve for x. Don't round until the final answer, and then round to 4 decimal places.

x=1.6397

200

e^4x=6

0.448=x

300

2^-2x= 1/16

x=2

400

2^x+2=9^x

0.922=x

500

The amount of a certain radioactive material (in grams) in a storage facility at time t is given by 

C(t)=53e^−0.11t  , where time is measured in years.

(a) How much of the radioactive material was present initially?

(b) What is the half-life of the radioactive material? (Hint: For what value of t is C(t)=26.5?) ( +100 Points)

a) 53 grams

b) 6.3 years.

Logarithms

100

log₅ 625= 4. Convert to the equivalent exponential form.

5⁴=625

200

2logx + 7logy. Condense the equation.

log(x²y⁷)

300

3logx + 8logy - log 3. Condense the Equation.

log ((x³y⁸)/3)

400

log ((2x⁴y⁵)/z⁸). Expand the expression.

log 2 + 4logx + 5logy - 8logz

500

log₇730=x. Solve for x. Round to 6 decimal places.

(hint: lnx/lna)

x=3.388155

Logarithms pt. 2 (worth +100)

100

log₇sqrt(7) = x. evaluate/solve for x without using a calculator.

( hint:how do we cancel out n² using another exponent?)

x=1/2

200

ln (1), find the value of the logarithm.

ln(1) = 0 

300

ln(3x+16)-lnx=ln4

x=16

400

ln(3x+25)=ln(2x+14)

(hint: remember to check your work!)

no solution ("-11")

500

The average annual expenditures for a country's consumers of dairy products can be approximated by the function 

g(x)=35.8 + 141.6lnx, where x= 10 corresponds to 2010.

a) find 2014 and 2018.

b) (extra 100 points) assuming the model remains accurate, what is the first year where expenditures exceed $485?

a) g(14)=409.49, g(18)=445.08

b) x= 23.86, therefore the first year to exceed is x=24, or 2024.

Simple + Compound Interest

100

Wilma borrowed $13,000 from her uncle to buy a used car. Her uncle charged simple interest at 2.4% for 55 years. Find the total amount (principal and interest) that Wilma paid to her uncle. 

FV= $14,560

200

$15,000 at 7% compounded monthly for 13 years. (hint: keep i as a fraction)

compound interest equation: FV=PV(1+i)ⁿ

FV=371,166.44

300

$6300 at 6% compounded quarterly after 9 years.

a) find the compound amount after 9 years

b) find the amount of interest earned (+100 points)

a) $10,767.58

b) $4,467.58

400

3% compounded quarterly. Find the APY.

(hint: APY= (1+ i)^m-1 )

APY/ re= 3.03%

500

Find the future value for the ordinary annuity with the given payment and interest rate.

PMT=$1,600; 1.95% compounded monthly for 2 years. 

(hint: FV= PMT[((1+i)^m-1)/i]

FV= 39126.22