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Growth and Decay
Logarithmic Equations
Logarithm Properties
Exponential Equations
Logarithmic Functions (as inverses)
100

In the equation y=ab^x, b=11/4. Is b a growth or decay factor?

b is a growth factor because in the equation y=ab^x b indicates growth if b>1.

100

Find the value of a for which the graph of y=ab^x is a horizontal line

a=0

100

Solve for x: 2log(10)=x

x=2-since there is no specified base, the base is 10. Using the Power Property, we can raise 10 to the 2nd power which equals 100. This means 10^x =100, so x=2.

100
Solve: 10^2x = 10,000
x=2-10,000 equals 10^4, so 2x=4 and x=2.
100
Evaluate logarithm log 10,000,000
7
200

Does this function show exponential growth or decay? y=(.5)*2^x

Exponential growth

200

Find the amount compounded annually for the given conditions -  Principal: $950 Interest: 5.1% Time: 3 years [Round to the nearest hundredth]

$1,102.89

200

Expand: log(ab/xy)

[log(a) + log(b)] - [log(x) + log(y)]

200

Give an example of the Change of Base Formula using log(M)

answers may vary


200

Sketch a graph y=-log(x+2)

See graph. 

300

In 2000, the annual rate of increase in the Snorlax population was exactly 3.49%. What is the growth factor for the Snorlax population?

b=1.0349

300
Write the exponential function for points (1,6) (0,2)
a=2 b=3 therefore 2(3)^x
300
Simplify this expression: log(100) - log(1)
log(100) - log(1)=2-there are two ways to solve this problem: 1) use the Quotient Property of Logarithms to change the expression into log(100/1) and simplify or 2) use the fact that when y=1, x must equal 0, so log(1)=0 and the expression is simply log(100).
300

Solve for x: 3^7x = 2500

x=[log base3 (2500)]/7

300
Graph y= log base4 (x)
See Scott for graph
400

Write an exponential function for a graph that includes (2,4) and (3,16)

y=(.25)*(4)^x

400
Unknown radioactive substance has a half life of 92 years. When will 0.01% of the substance remain?
1222.5 years
400
Simplify: (log 45 (logθ (log2 (log3 (log10 1,000,000,000))))) where θ=a non-right angle of an isosceles right triangle
No solution-logθ(1)=0 and logx(0)=undefined.
400

Solve for x: ln(3x)=8

(e^8)/3

400
Find domain and range of the graph of the function y= log (x-2)+1
x>2 y= all real numbers
500

John's garden has 80 pieces of grass. Two hours later, his garden has 120 pieces of grass. If grass grows at an exponential rate, how much time will it take for John to have 220 pieces of grass?

Around 2.989 hours


500

If you invest $2000 in an account earning 3% interest compounded annually, how long will it be until you have $2500?

7.44 years

500
Simplify: 10 ∑ log2(k) k=1 where log2(3)=1.585, log2(5)=2.322, and log2(7)=2.807
The expression simplifies to 21.791- log2(6)= log2(2) + log2(3) because of the Product Property of Logarithms, 9=3x3, and 10=2x5.
500

27^x+4=(1/9)^4x-12 Solve for x

What is x=12/11

500

Find inverse of function: y= 2 * 5^x-3

y=log base5 (x/2) +3