Exponential Equations with Logarithms

You invest $15,000 with an interest rate of 8% per year compounded continuously. The function A\left(t\right)=15000e^{0.08t} models the situation. What set up will allow you solve for how long it will take for the investment to grow to $45,000 ?

• 45000=15000e^{0.08t}

• A\left(3\right)=15000e^{0.08\left(3\right)}

• A\left(45000\right)=15000e^{0.08\left(45000\right)}

• 3=15000e^{0.08t}

• Divide both sides by 3

• Divide both sides by e

• Take the natural log of both sides

• Rewrite the exponent 0.08t as the coefficient of "e"

• Subtract e to both sides

An amount of $2,000 is deposited into a bank paying an annual interest rate of 2.85% compounded continuously. How long will it take for the money to double?

• 21.22 years

• 24.32 years

• 20.12 years

• 24.67 years

• 0.542

• 2.215

• 4.023

• 2.794

• 5
• 13
• 84
• -20

log₅(4x-7)=log₅(x+5)

• 3

• 12

• 4

• 7

log₂(x+3)=4

• 16

• 13

• 3

• 10

Solve for x:

log₈(4x+4)=2

• 15

• 12

• 10

• 3

log₄ x = 3

• 4

• 12

• 32

• 64

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e