Exponential Growth & Decay and Compound Interest

Growth: goes up in value, use this formula! y = c(1+r)t 1+r>1 Decay: goes down in value, use this formula! y = c(1- r)t 1- r <1

Identify the following as growth or decay You are checking the part being raised to the power -bigger than 1 is growth -between 0 and 1 is decay y = 500(1.20)5 y = 375(.078)t y = 5(1.078)6 y = 30(.99)4

Example: You buy a new 10 speed bike for $150. It loses value at a rate of 15% per year. What is it’s worth in 3 years? Worth = cost(rate)years w = c(1-0.15)3 (a loss means –15%) w = 150(.85)3 w = 92.12 The bike was only worth $92.12 in 3 years.

Write a general equation for the following You purchased a car for $35,000. The minute you drove it off the lot it started going down in value by 1.3%. Write an equation for its value in the future. You just purchased a painting as an investment and it is suppose to appreciate it value at a rate of 3.65% each year. Write an equation for its value in the future. f(t) = 35,000(0.987)t f(t) = P(1.0365)t

Simple interest p(t)= p0 + p0 rt (will be a linear function) To find the amount of interest you earn use I=prt To find the total amount you have use A=p+prt p(t)= p0 + p0 rt I = interest A or p(t) = total amount you have p or p0= principal amount you start with r = rate of interest (write % as a decimal) t= time in years

You have $3,150 after one year. If you invest $3,000 at 5% for one year, how much will you make for the year? I = prt I = 3000  0.05  1 I = 150 You made $150 for the year. p(1)= p + prt p(1)= 3000 + 3000  0.05  1 p(1)= 3150 You have $3,150 after one year.

(will be an Exponential Function) Compound Interest (will be an Exponential Function) Compound interest formula: A = p(1+r)t p(t) = p0(1+r)t A or p(t) = total amount you have p or p0= principal amount you start with r = rate of interest (write % as a decimal) t= time in years

Find the total amount in your account if you start with $750 at 7 Find the total amount in your account if you start with $750 at 7.5% interest compounded annually for 2.5 years. A = p(1+r)t = 750(1+0.075)2.5 (Plug in what you know) = 750(1.075)2.5 (simplify) = $898.63

A = p(1+r)t (Plug in what you know) 200 = p(1.07)5 (then isolate p) How much should you invest at 7% compounded annually to have $200 after 5 years? A = p(1+r)t (Plug in what you know) 200 = p(1.07)5 (then isolate p) 200 = p (1.07)5 142.60= p

You put $100 in the bank at 4% interest compounded annually and leave it until you are 60. Write a function to show how much money will you have as a function of time in years and solve. f(t) = p(1+r)t f(46) = 100(1.04)46 (This assumes you are currently 14) f(46) = 607.48 You will have $607.48 when you are 60

What if you put the same $100 in a mutual fund that pays 10% interest compounded annually until you’re 60? Write a function to show how much money will you have as a function of time in years and solve. f(t) = p(1+r)t f(46) = 100(1.10)46 f(46) = 8017.95 You would have $8,017.95 when you are 60