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Use your calculator to write the exponential function.PowerPoint Presentation

Use your calculator to write the exponential function.

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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

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