Question

Ken has a food truck that sells for 5 dollars and up. Bryan buys $20 worth of food. How much money will Ken make in one hour if the price of the food goes up by $10 every 2 minutes and 30 seconds for the tourist visits

Answer 1

Let:

M(t) = Money earned by ken as a function of time

Let's asume ken earned 20 dollars for the purchase of Bryan

And let's make a conversion:

2 min * 60 s/1min = 120s

So, the food goes up every 150s

Hence the function M(t) would be:

Let's define t2= 150s

M(t) = $20 + ($5+$10t/t2)

Because he sells his food for $5 and the price goes up by $10 every 150s

Ok, now an hour has 3600s:

So:

3600s/150s = 24

We can conclude that in one hour the food went up in price 24 times

Now, using the function:

M(t) = $20 + ($5+$10t/t2)

For t = 3600

M(3600) = $20 + ($5 + $10 * (3600)/(150))

M(3600) = $20 + ($5 + $10*24)

M(3600) = $20 + $5 + $240 = $265

Ken will make $265 in one hour