Exponential Functions
Log Functions
Properties of Logs
Log & Exponential Equations
Financial Models
100
1. Is the function represented by the table below linear, exponential, or neither?
2. Write the equation for the function.
1. Exponential.
2. f(x) = 20(0.5)x
100
Rewrite as a logarithm: 25 = x + 1
log2 (x+1) = 5
100
Suppose ln 2 = a and ln 3 = b, use properties of logs to write ln 0.5 in terms of a and b.
-a
100
Solve for x:
log x + log (x + 15) = 2
x = 5
100
How much money would you make if you invest $100 at 5% interest compounded monthly after a period of 3 years?
$116.15
200
Write an equation for the exponential function represented by the graph below:
g(x) = -6x
200
Rewrite as an exponential equation: ln 7 = 2x
e2x = 7
200
Find the exact value of:
3
200
Solve for x:
log8 (x + 6) = 1 - log8 (x + 4)
x = -2
200
How much money would you make if you invest $500 at 7.25% interest compounded continuously after a period of 1.5 years?
$557.44
300
Solve for x:
x = 2, x = 4
300
Find the domain of h(x). Express your answer using interval notation.
h(x) = 1 - 3 log2 (5x + 2)
x ∈ (-2/5 , ∞)
300
Expand:
log x + log (x + 2) - 2log (x + 3)
300
Solve for x. Leave your answer in exact form.
8-x = 1.2
-log8 1.2 = x
300
How many years will it take for an initial investment of $25,000 to grow to $80,000? Assume a rate of interest of 7% compounded continuously. Round your answer to the nearest thousandth.
16.616 years
400
1/27
400
Solve for x: log3 243 = 2x + 1
x = 2
400
Condense into a single log:
log2 [x(3x - 2)4]
400
Solve for x. Leave answers in simplified, exact form.
31-2x = 42+x
x = [ln (3/16) / ln (36)]
400
How long does it take for an investment to triple in value if it is invested at 6% compounded semiannually? Round your answer to the nearest thousandth.
18.584 years
500
Solve for x. Leave answer in exact form.
x = 19/11
500
Solve for x. Leave your answer in exact form:
8(10)2x-7 = 3
x = [7 + log (3/8)] / 2
500
3
500
Solve for x:
52x + 5x+1 - 50 = 0
x = 1
500
On January 1, Kim places $1,000 in a certificate of deposit (CD) that pays 6.8% compounded continuously and matures in 3 months. Then, she places the $1,000 and the interest from the CD in a passbook account that pays 5.25% compounded monthly. How much does Kim have in the passbook account on May 1?
$1,021.60