In a country where inflatoin is a concern, prices have risenby 21% over a 6-year
ID: 3089267 • Letter: I
Question
In a country where inflatoin is a concern, prices have risenby 21% over a 6-year period. a) by what percent do the prices rise each year? b) low long does it take for prices to riseby 3%? c) use a continuous growth rate to model inflation by apunction of the form P = Poekt. In a country where inflatoin is a concern, prices have risenby 21% over a 6-year period. a) by what percent do the prices rise each year? b) low long does it take for prices to riseby 3%? c) use a continuous growth rate to model inflation by apunction of the form P = Poekt.Explanation / Answer
if the prices have risen by 21%, then the final price can berepresented by 1.21 where the initial price is just 1 1.21 = 1*e^(kt) if we want to solve for k we can plug in t = 6 years, and take thenatural log of both sides ln(1.21) = k(6) k = ln(1.21)/6 = .03177 so now we can plug it back into the equation, and we get P =e^(.03177*t). this is part C we can use this equation and values that the question gives us, toanswer the first two parts in one year, t = 1, so just plug that into the equation P = e^(.03177 * 1) = e^(.03177) = 1.0328, or about 3.28% above whatit started in order to raise 3%, set the final value to 1.03, then solve fort 1.03 = e^(.03177*t) natural log both sides, ln(1.03) = .03177 * t t = ln(1.03) / .03177 = .9304 years