use your calculator to write the exponential function. bell work time0123 value318108648
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USE YOUR CALCULATOR TO WRITE THE EXPONENTIAL FUNCTION.
Bell Work
Time 0 1 2 3
Value 3 18 108 648
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Objective
F.LE.5: I will identify common ratio (b) and initial value (a) of from a given context.
xy ab
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Things to Remember
*Exponential growth (b>1)
a = initial Value r = Rate (often as a percent written in decimal) b = change Factor x = number of time periods
(1 )xay r *Exponential Decay 0 < b < 1 (1 )xay r xy ab
Exponential function
1 r
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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 = change Factor: __________________________________
Function: __________________________________
$500
8% = 0.08
1 r 01 0. 8 1.08xy ab 500 1 8 .0
xy
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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
xy ab 1 8500 .0
xy
500 11000 .08x
2 1.08x
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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.
2 1.08x
52 1.08
1.4 32 693
102 1.08
2.1 22 589
92 1.082 1.999
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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 = change Factor: _____________________________
Function: __________________________________
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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
xy ab