Use your calculator to write the exponential function
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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

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Use your calculator to write the exponential function

Use your calculator to write the exponential function.

Bell Work


Objective

Objective

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


Things to remember

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

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

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 cont1

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

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 applications1

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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