Logarithms to Exponential Applications

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

What is the domain?

• (-∞, ∞)

• (0, ∞)

• [1, ∞)

• (1, ∞)

Where is the asymptote?

• x = 1

• y = 1

• x = -1

• y = -1

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

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

• x = 2

• x = -2

• y = 2

• y = -2

What is the domain and range of
f(x) = log ₃ (x + 1)?

• D: (− ∞, ∞) R: (−1, ∞)

• D: (− ∞, ∞) R: (1, ∞)

• D: (−1, ∞) R: (− ∞, ∞)

• D: (1, ∞) R: (− ∞, ∞)

Classify the following graph.

• Exponential Growth

• Exponential Decay

• Logarithmic

Change to exponential form. log_a2 = 5

• a² = 5

• 5² = a

• a⁵ = 2

• 2⁵ = a