Exponential Growth and Decay

Exponential Growth and DecayM & M LabPart 1- GrowthWhat happened to the number of M&Ms?Part 2-DecayWhat happened to the number of M&Ms?

IncreasedDecreasedWhat was true about the values of a &b?What was true about the values of a &b?a is the starting number of M&Msb >1a is the starting number of M&Msb < 110.1 Exponential FuntionsEx. 1 Sketch the graph of y = 2x. Then state the functions domain & range.*Sketch of graph must have y-intercept & four other coordinate points. Use the table function on your TI-83!

xy-20.25-10.5011224Ex. 2 Sketch the graph of y = ()x. Then state the functions domain & range.

xy-21.3061-11.14290110.87520.76563decayExponential Growth Model

Instead of x, t is the variable.(1+r) is called the growth factor. a is the initial amount. y is the amount after t years.Exponential GrowthCompound Interest

A is the balance.

P is the principal deposited in an account.

r is the interest rate changed to a decimal (% 100).

n is the number of times the interest is compounded in a year. Annually n = 1Semiannually n = 2Quarterly n = 4 Monthly n = 12Compound Interest ProblemYou deposit $500 in an account that pays 3% interest. Find the balance after 2 years if the interest is compounded quarterly.

A = ?P = $500

Exponential Decay Model

y is the quantity after t years. t is the variable.

a is the initial amount.

(1-r) is the decay factor.Exponential DecayDepreciationYou buy a new car for $22,000. The value of the car decreases by 12.5%. What is the value of the car after 4 years.

y = ? a = $22,000