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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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Presentation Transcript
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