Answer:
Y(t) = 190*e^{5*0,04}
Explanation:
Exponential equations, are very helpfull tool when dealing with growing or decaying process. The most common shape of such equatio is:
Y(t) = Y₀*e^{kt}
In that equation:
Y(t) would be the value of Y ( whatever the situation is ) at certain time t
Y₀ stand for value of Y at the time t =t₀ = start of the evaluating process
e is the well known number = 2.718
k is a parameter (indicator of the number of units in which the rate of growing is measured ( in our case the rate of growing in % is 4 we have to express it as a number 0,04 and the number of years is 5 from 2005 up to 2010, taken into account the day and the month is the same for the two measured)
t is the rate of growing or decaying of the process.
In our particular case we have
Y(t) would be the cost of a cart of groceries at time t
Y₀ is the value of Y when t = 0 one day in 2005
Hear we have to be aware of the fact that problem statement does not identify exact date but only years , and the rate of inflation is given per year. So we have to assume that dates are over the same day and month in order to have a complete year for the rate of growing.
If we do so (for instance from 12-06-2005 and 12-06-2010) we get 5 complete years and are able to say that we are dealing with complete 5 years.
Then our final equation is
Y(t) = Y*e^kt} Y(t) = 190*e^{5*0,04}