Use your calculator to write the exponential function. Time 1 2 3 Value 18 108 648 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 function *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 Decay 0 < b < 1 Exponential function

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

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 – 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 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