Use your calculator to write the exponential function.

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# Use your calculator to write the exponential function. - PowerPoint PPT Presentation

Use your calculator to write the exponential function. Bell Work . Objective . F.LE.5: I will identify common ratio (b) and initial value (a) of from a given context. Things to Remember. *Exponential Decay 0 &lt; b &lt; 1. *Exponential growth (b&gt;1) a = initial Value

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### Use your calculator to write the exponential function.

Bell Work

Objective
• F.LE.5: I will identify common ratio (b) and initial value (a) of from a given context.
Things to Remember

*Exponential Decay 0 < b < 1

*Exponential growth (b>1)

• a = initial Value
• r = Rate(often as a percent written in decimal)
• b=change Factor
• x = number of time periods

Exponential function

Example 1:Using Exponential Applications
• An investment starts at \$500 and grows exponentially at 8% per year.

Part A: Write a function for the value of the investment in dollars, y, as a function of time, x, in years.

• Solution:

a = initial Value: ______________

r = Rate: ________________

b=changeFactor: __________________________________

Function:__________________________________

\$500

8% = 0.08

Example 1:Using Exponential Applications – Cont.

An investment starts at \$500 and grows exponentially at 8% per year.

• Part B: After how many years it will take to double up?
• Solution:

Asking ... when will it be worth \$1000?Which is the total value (y) after x number of years

Example 1:Using Exponential Applications – Cont.

Part B: After how many years will it take to double up?

• Solution:Use trial and error to find x.

when x = 5

too low

when x = 10

too high … keep narrowing it down!

when x = 9

Ok … that’s close enough.

It will take about 9 years to double.

Example 2:Using Exponential Applications
• A car bought for \$13,000 depreciates at 12% each year.
• Part A: Write a function for the value of the car in dollars, y, as a function of time, x, in years.
• Solution:

a = initial Value: ______________

r = Rate: ________________

b=changeFactor: _____________________________

Function:__________________________________

Example 2:Using Exponential Applications

A car bought for \$13,000 depreciates at 12% each year.

• Part B: After how many years will the price be less than \$5,460?
• Solution:

Asking ... when will it be less than \$5,460? Which is the total value (y) after x number of years