USE YOUR CALCULATOR TO WRITE THE EXPONENTIAL FUNCTION.

Bell Work

Time 0 1 2 3

Value 3 18 108 648

Objective

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

xy ab

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

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

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

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

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: __________________________________

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