SOLUTION: The predicted price P, in dollars, of an item can be modeled by the function P (t ) = P0(1.035)t , where P0 is the initial price of the item and t is the amount of time, in years,

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The predicted price P, in dollars, of an item can be modeled by the function P (t ) = P0(1.035)t , where P0 is the initial price of the item and t is the amount of time, in years,      Log On


   

Question 1203317: The predicted price P, in dollars, of an item can be modeled by the function P (t ) = P0(1.035)t ,
where P0 is the initial price of the item and t is the amount of time, in years, after the initial price was established. Based on the model, if the price of one gallon of milk is expected to be $4.69 in the year 2020, in which of the following years will the price of one gallon of milk be closest to $3.95 ?
(A) 2009 (B) 2010 (C) 2014 (D) 2015 (E) 2025
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Write the function better than that. Maybe you want to show as P%28t%29=P%5Bo%5D%281.035%29%5Et . There is still the feeling that the description or the function is not written properly.

Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.

From the problem, we have this equation

    3.95 = 4.69%2A1.035%5Et


We transform it in a standard way

    3.95%2F4.69 = 1.035%5Et

    0.842217 = 1.035%5Et.


Then take logarithm base 10 of both sides

    log%28%280.842217%29%29 = t%2Alog%28%281.036%29%29


and find t

    t = log%28%280.842217%29%29%2Flog%28%281.035%29%29 = -4.99158


which we round to 5 years.


So, the event under the problem's question happened 5 years before the year 2020.


ANSWER.  The closest year is 2015, option (D).

Solved.