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## 1) y = 5000(1 + .06) 4

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**1) y = 5000(1 + .06)4**Variable by itself Type in calculator 6312.4 2) 5000 = A(1 + .06)4 Variable times something Divide by everything 5000/(1.06)4 3960.47 3) 5000 = 2000(1 + .06)x Variable is exponent 5000/2000 1.06x Logs Log(2.5) = x log 1.06 Log(2.5)/log 1.06 = x 15.73 4) 5000 = 2000(1 + r)4 Variable has exponent 5/2 = (1 + r)4 Take nth root 1.257 = (1 + r)so r = .257 or 25.7%**The formula to find money compounded is given by the**following formula: A = P(1 + r/n)ntwhere n is the number of times per year, r is the rate, and t is the years, P is the principal. Quarterly: n = 4; bi-weekly: n = 26; semi-monthy: n= 24 Find how much 500$ will be in 10 years if you invest into an account that compounds it monthly at 5%? 2) How long will it take you to double your money invested at 5.35% compounded it quarterly. 3) Find out how much money you need to invest if there will be $1600 after 5 years if compounded weekly at 4%? 4) What is the rate if $3500 becomes 5000$ compounded monthly for 7 years?**Find how much 500$ will be in 10 years if you invest into an**account that compounds it monthly at 5%? 2) How long will it take you to double your money invested at 5.35% compounded it quarterly. 3) Find out how much money you need to invest if there will be after 5 years if 1600$ is compounded weekly at 4%? 4) What is the rate if $3500 becomes 5000$ compounded monthly for 7 years?**Remember that compounded continuously is A=Pert**1) How much should you invest now so that you have $160,000 in 18 years if money is compounded 4% continuously? 2) What is the rate if it takes 12 years to double your money compounded continously?**Ex) A Snickers candy bar was $.25 in 1980. It was $.85 in**2008. What is the rate of inflation? (0, .25) and (28, .85). Exp regression and you get y=.25(1.047)x. So it’s 4.7% growth Or .85= .25(1 + r)28 3.4 = (1 + r)28 28th root of 3.4 is 1.044 so 4.7% 5) In 1930, the cost of toothpaste was $.05. In 2008, the cost was $1.25. A) What is the rate of inflation? B) Predict when the toothpaste will be $1.60 6) In 1971 the first Starbucks Opened. Now there are 19,555 stores worldwide. • What is the rate of growth • Predict how many Starbucks there will be in 2020 if the trend continues**Half Life: y = a(1/2)t/k where y is the final amount, a is**the initial amount, t is the time in years and k is the amount of years for it to be ½ of its value. • What is the exponential equation for an unknown substance that has a ½ life of 1000 years? 19) A person’s body’s half life is about 20 years. How long has the body been in the ground if 1/6 of the body is remaining? 20) The ½ life of Carbon-14 is 5760 years. Suppose that a piece of pottery has been in the ground for 5000 years. What % of Carbon-14 is remaining? 21) The ½ life of Carbon-14 is 5760 years. If 1/8 of a sample survives, how long was it in the ground?