Without graphing, determine whether the function represents exponential growth or decay.
f(x)=2(0.65)^x
Exponential Decay
100
Write the equation in logarithmic form.
10^3= 1000
log1000=3
100
Write the expression as a single logarithm.
log(4)2+log(4)8
log(4)16
100
Solve the equation
2^x=8
3
100
Write the expression as a single natural logarithm.
ln16-ln8
ln2
200
Without graphing, determine whether the function represents exponential growth or decay.
y=0.45(3)^x
Exponential Growth
200
Evaluate the logarithm.
log(4)2
1/2
200
Write the expression as a single logarithm.
log(6)5+log(6)x
log(6)5x
200
Solve the equation. Round to the nearest ten thousandth.
9^2y=66
y=0.9534
200
Write the expression as a single natural logarithm.
3ln3+ln9
ln243
300
Write an exponential function to model each situation. Find the amount after the specified time.
A population of 120,000 grows 1.2% per year for 15 years.
Use the formula: A(t)= a(1+r)^t
143,512
300
Write the equation in exponential form
log(4)1=0
4^0=1
300
Expand the logarithm.
log(7)49xyz
log(7)49+ log(7)x+ log(7)y+ log(7)z
300
Solve the equation. Round to the nearest ten thousandth.
25^2x+1=144
x=0.2720
300
Solve the equation. Round answer to nearest hundredth.
2ln(3x-4)=7
x=12.37
400
Identify the meaning of the variables in the exponential growth or decay functions.
A(t)=a(1+r)^t
a= initial amount
r= rate of growth or decay
t= number of time periods
400
Evaluate the logarithm log10,000
4
400
Use the Change of Base Formula to evaluate the expression.
log(12)20
≈1.2
400
Solve the equation.
log(3x+1)=2
x=33
400
Use ln to solve the equation. Round answer to nearest hundredth.
e^x=15
x=2.71
500
A population of 752,000 decreases 1.4% per year for 18 years.
A(t)=a(1+r)^t
583,448
500
Use this method to write the equation in logarithmic form.
3^4=81
4= log(3) 81
500
Use the properties of logarithms to evaluate the expression.
log(2)4- log(2)16
-2
500
Solve the equation.
log(5-2x)=0
x=2
500
Solve the equation. Round to nearest thousandth.
e^x/4 - 3= 21