Question

An item costs $500 at time t=0 and costs $P in year t. When inflammation is r% per year, the price is given by P = 500e^(rt/100)

a) if r is a constant, at what rate is the price rising ( in dollars per year)
1) initially 2) after 2 years
b)now suppose that r is increasing by 0.3 per year when r=4 and t=2. At what rate is the price
increasing at that time?

I can do part a) of this question but cant figure out the solution to part b).

Answer 1

inflammation?

Answer 2

inflation not inflammation sorry

Answer 3

b) use product rule

Answer 4

show me your work for part a) first

Answer 5

nice pic

Answer 6

dp/dt = 5re^(rt/100) so initially is 5r dollars/year and after 2 years 5re^(r(2)/100)

Answer 7

good

Answer 8

now suppose r is not constant

Answer 9

yea what do I do with 0.3

Answer 10

do I do the dP/dt again with r=0.3?

Answer 11

what?*

Answer 12

so I assumed that r is a function of time