i don't understand this word problem.
Barnany's godfather is alway complaining that back when he was a teenager, he used to be able to buy his girlfriend dinner for only $1.50
a) If that same dinner that Barnaby's grandfather purchased for $1.50 sixty years ago now costs $25.25, and the price has increased exponentielly, write and equation that will give you the costs at different times.
b) How much would you expect the same dinner to cost in sixty years?
see other post.
To understand the word problem, let's break it down step by step:
a) If we assume that the price increase of the dinner over time follows an exponential growth pattern, we can use the general form of an exponential equation: y = a * (1 + r)^x, where:
- y represents the current price of the dinner,
- a is the initial price of the dinner (in this case, $1.50),
- r is the growth rate (expressed as a decimal), and
- x represents the number of years that have passed.
So, let's substitute the given values into the equation:
y = 1.50 * (1 + r)^x
The problem states that sixty years ago, the dinner cost $1.50 and now it costs $25.25. Let's use this information to create an equation:
25.25 = 1.50 * (1 + r)^60
b) To determine the expected cost of the dinner in sixty years, we can use the equation we derived in part a and solve for the future price. Rearranging the equation, we have:
(1 + r)^60 = 25.25 / 1.50
Now, let's solve for (1 + r) first:
(1 + r) = (25.25 / 1.50)^(1/60)
Finally, we can calculate the future cost of the dinner using the value of (1 + r):
Expected cost in sixty years = a * (1 + r)^60
Substituting the given initial price (a = $1.50):
Expected cost in sixty years = 1.50 * ( (25.25 / 1.50)^(1/60) )