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=abx 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-in an exponential function y=(a)*b^x, b is growth or decay factor. when b>1, b is a growth factor. when 0
200
Find the amount continuously compounded for the given conditions
Principal: $950 Interest: 5.1% Time: 3 years
[Round to the nearest hundredth]
$1107.06
200
Expand: log(ab/xy)
[log(a) + log(b)] - [log(x) + log(y)]-go expand ab and xy, we use the Product Property which states log(ab)=log(a)+log(b). To do the division, we use the Quotient Property which states log(a/b)=log(a)-log(b).
200
Give an example of the Change of Base Formula using log(M)
log(M) = [log base4 (M)]/[log base4 (10)]
200
Match function with inverse
y=-log base17 (x)
y=17^-x
(See Scott for explanation of answer)
300
In 2000, the annual rate of increase in the Filipino population was exactly 3.49%. What is the growth factor for the Filipino population?
b=1.0349-a growth factor can be derived from b=1+r (where r is the rate). decay factors can be derived from b=1-r.
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
Isolate x in terms of logs (no calculator): 3^7x = 2500
x=[log base3 (2500)]/7-solve by taking the common log of both sides, using the power property, dividing, using the change of base formula, then dividing again.
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-See Ziggy for explanation
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
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-See Ziggy for explanation.
500
If you invest $2000 in an account earning 3% interest compounded continuously, 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 3^3(x+4)=3^-2(4x-12)
3x+12=-8x+24
11x=12
x=12/11