Exponential and Logarithmic Applications

Growth or Decay?

P = 250(0.87)^t

• Growth

• Decay

Which of the 4 choices below is FALSE:

• P(t) is the quantity at time t

• P₀ is the initial quantity

• 0.04 is the exponential growth rate

• 0.04 is the exponential decay rate

Growth or Decay?

y = 3+4(2^4t)

• Growth

• Decay

Which of the following represents the graph of an exponential growth function?

• A line that passes through the origin.

• A curve that approaches the x-axis as it moves left and rises steeply to the right.

• A curve that starts high on the left and approaches the x-axis as it moves right.

• A parabola that opens upwards.

• Product Rule

• Quotient Rule

• Power Rule

• Change of Base Rule

Evelyn, Michael, and Benjamin are on a treasure hunt. They found a cryptic note that says 'To find the treasure, solve this: What is the inverse of f(x)=5^x+3?'. Can you help them solve it?

• f^-1(x)=log₃(x-5)

• f^-1(x)=log₅(x)-3

• f^-1(x)=log₅(x-3)

• f^-1(x)=log₅(x+3)

Emma, Priya, and Benjamin are on a treasure hunt. They found a mysterious note with the function f(x)=5^(x+2) written on it. They believe it's a clue and need to find the inverse of this function to proceed. Can you help them?

• f^-1(x)=log₅(x-2)

• f^-1(x)=log₅(x)-2

• f^-1(x)=log₅(x)+2

• f^-1(x)=log₅(x+2)

What is the domain of the function shown?

• (-∞, ∞)

• (0, ∞)

• [1, ∞)

• (1, ∞)

What is the domain and range of the function y=2^x ?
Use the graph to help!

•  Domain: −∞<x<∞
  Range: y>0

• Domain: −∞<x<∞
  Range: y>1

• Domain: −2<x<∞
  Range: y>0

• Domain: −∞<x<∞
  Range: y>0

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)

• log₂(xy⁵)

• log₂(x/y)⁵

• log₂(x/5y)