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Use your calculator to write the exponential function.

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.

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  1. Use your calculator to write the exponential function. Bell Work

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

  3. 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

  4. 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

  5. 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

  6. 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.

  7. 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:__________________________________

  8. 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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