Exponential Growth vs. Decay: Quick Warm Up

Interact with this app for a minute or two. Be sure to move the LARGE POINT and slider. Then answer the questions that follow.

Can we see the initial amount in the equation of an exponential growth or decay curve? If so, where is it?

Suppose we have an equation of the form [math]y=a\cdot b^x[/math]. What is the initial amount (in terms of [i]a[/i] and/or [i]b[/i])?

Suppose we have an equation of the form [math]y=a\cdot b^x[/math], where [i]a[/i] > 0 & [i]b[/i] > 0. [br]Without looking at its graph, we tell for sure if the curve is an exponential growth curve or exponential decay curve? Explain.

Suppose a $3 item increases in value by 29% per year. Which of the following statements are true?

The equation to model this would be [math]y=0.78\cdot3^x[/math] The equation to model this would be [math]y=3\cdot0.71^x[/math] The equation to model this would be [math]y=3\cdot1.29^x[/math] The equation to model this would be [math]y=1.29\cdot3^x[/math]

Suppose [i]y[/i] = the value of an item after [i]x[/i] years. And suppose [math]y=5\cdot0.75^x[/math]. Which of the following statement(s) are true?

The item decreases in value by 25% each year. The initial value of the item is $5. For every year that passes, the value of the item is worth 75% of what it was the previous year. The initial value of the item is $0.75.

Exponential Growth vs. Decay: Quick Warm Up

Interact with this app for a minute or two. Be sure to move the LARGE POINT and slider. Then answer the questions that follow.

Information: Exponential Growth vs. Decay: Quick Warm Up