Growth and Decay
In the following exponential function, identify the asymptote.
y = 2x - 1 - 5
y = -5
You deposit $3,000 into an account the earns 4% annual interest. Find the balance of the account after 5 years.
$3649.96
Rewrite the following in logarithmic form.
93 = 729
log 9 (729) = 3
Solve the following exponential equation. Write your approximate answer.
3x = 24
2.892789261
Simplify.
(3x4y2)3
27x12y6
In the following exponential function, identify the domain and range.
y = 4(1/2)x+1 + 3
Domain: (-∞, ∞)
Range: (3, ∞)
You deposit $2500 in an account that pays 3.5% interest compounded continuously. What is the balance after 8 years?
$3,307.82
Rewrite the following in exponential form.
ln (1) = 0
e0 = 1
Solve the following exponential equation. Write your approximate answer.
-3e2x + 14 = 5
0.5493061443
Simplify.
-4x-5yz3 • 6xy4z-4
-24y5/(x4z)
In the following exponential function, identify the domain and range.
y = -3(2)x - 4 + 1
Domain: (-∞, ∞)
Range: (-∞, 1)
You deposit $1500 into an account that pays 7% interest compounded daily. Find the balance after 15 years.
$4,286.05
Expand the following logarithmic expression.
log 7 (3x2yz4)
log 7 (3) + 2 log 7 (x) + log 7 (y) + 4 log 7 (z)
Solve the following logarithmic equation.
(1/4) log 2 (5x + 2) = 1.25
x = 6
Solve the following equation.
(x+3)4/3 - 10 = 6
x = 5
The exponential function: A(Area) = A0e-0.35t
is a common model used to represent the healing of a wound over time. In this model, A0 represents the wounds original size and t represents the number of days following the occurrence of the injury/wound.
Suppose that a wound initially had an area of 100 square millimeters. How large will the area be after 10 days?
3.02 square millimeters
The value of a snowmobile has been decreasing 7% each year since it was new. After 3 years, the value is $3000. Find the original cost of the snowmobile.
$3729.69
Condense the following logarithmic expression.
log 3 (5) + 4 log 3 (w) - 7 log 3 (z)
log 3 (5w4/z7)
Solve the following logarithmic equation. Be sure to check for extraneous solutions.
log 2 (x) + log 2 (x - 14) = 5
x = 16
Solve the following radical equation. Be sure to check for extraneous solutions.
√(3x+40) = x+4
x = 3
Challenge: Using either a graphing calculator or your knowledge of solving exponential equations. Identify the (x,y) ordered pair where the following exponential growth graph and exponential decay graph would intersect.
y = 4x - 1 and y = (1/2)x - 6 - 1
(2, 15)
You invested a small savings into an account that earned 6.5% annual interest compounded semi-annually. After 14 years, the account has now grown to approximately $17,752.51. To the nearest whole dollar, what was the value of your initial investment?
$7,250
Expand the following logarithmic expression.
log 2 (8x5/3y4)
log 2 (8) + 5 log 2 (x) - log 2 (3) + 4 log 2 (y)
Solve the following logarithmic equation. Be sure to check for extraneous solutions.
log 3 (x) + log 3 (2x - 15) = 3
x = 9
Solve the following radical equation.
√(x + 7) = √x + 1
x = 9