Solving Exponential Equations
4x-1 = 43
X = 4
Solve for x:
Log4(64) = x
Rewrite this in logarithmic form:
4x = 64
Log4(64) = x
You have a 500 gallon tank of gas to heat your home. Every day, you use 12% of the remaining volume in the tank. Write this in exponential decay form.
A(t) = 500(1 - 0.12)t
What are the two types of exponential functions?
Exponential growth and exponential decay
X = 4
Solve for x:
Log2(512)= x
X = 9
Rewrite this in logarithmic form:
6x-4 = 9
Log6(9) = x-4
Salt dissolves in water at a rate of 25% each minute. After 10 minutes, how much salt will be left undissolved in the water if I placed 10 grams of salt initially in the cup of water?
A(10) = 0.56
What is the line that the output values of a graph seem to be approaching called?
An asymptote
32x = 27x-4
X = 12
Solve for x:
Log3(2x - 4) = Log3(8x + 14)
X = -3
Rewrite this in exponential form:
Log2(64) = x
2x = 64
Valentine’s Day spending is supposed to increase 5.22% annually from $25.9 billion in 2023. Write an expression that models this equation.
A(t) = 25.9(0.0522 + 1)t
What is the inverse of an exponential function?
A logarithm
55x = 125x+2
X = 3
Solve for x:
Log4(6x + 24) = Log4(10x - 18)
X = 10.5
Rewrite this in exponential form:
Logx(27) = 3
X3 = 27
After drinking a cup of coffee, the body has 100 mg of caffeine. The average person can eliminate about 12.5% of caffeine from their body every hour. Write and solve an equation determining the amount of caffeine in a person’s system after 6 hours.
A(t) = 100(0.875)t
A(6) = 44.88 mg of caffeine
A(t) stands for what?
Annuity, or the ending amount
(1/2)4x+1 = 82x+1
X = -5/2
Solve for x:
Log6(4x + 16) = Log6(12x - 2)
X = 2.25 or 9/4
Rewrite this in exponential form:
Log6(2x+4) = 3
63 = 2x+4
A swimming pool can fit 40,000 gallons of water. It has a leak, and is losing 0.25% of the volume per hour. At 72 hours, how much water is left in the pool?
A(t) = 40,000(1-0.0025)t
A(72) = 33,403.28 gallons
What is the base of the natural logarithm called?
“e”, or Euler’s Number