Question

Certain pieces of antique furniture increased very rapidly in price in the 1970s and 1980s. For example, the value of a particular rocking chair is well approximated by V=150(1.65)^t where V is in dollars and t is the number of years since 1975. Find the rate, in dollars per year, at which the price is increasing.

Answer 1

it increases by 150 * .65 per year

Answer 2

97.5 dollars per year increase

Answer 3

why wouldnt it be 150*1.65? because I did that and got it wrong.... but I'm not sure why

Answer 4

i might be wrong

Answer 5

Yeah... it's not working...

Answer 6

the reason why 150 * 1.65 is wrong is because that is how much TOTAL after one year

Answer 7

got it

Answer 8

that answer is 150 * (0.65)^t

Answer 9

the*

Answer 10

I feel like this should be easier than it actually is.... okay well then wouldn't I just have to plug in 5 for t? I should just get the answer that way (1975-1980)

Answer 11

I plugged it in and it's not working

Answer 12

also, thanks for your help!

Answer 13

what class is this for?

Answer 14

Calculus... and I took it in high school and thought over the summer it'd be easy as a refresher, but man is this much more difficult than I remember...

Answer 15

:) you'll get it. take the derivative of both sides :)

Answer 16

150(1.65)^t*ln(t)

Answer 17

but that's not working either

Answer 18

should I plug in 1 for t?

Answer 19

or 5?

Answer 20

or neither?

Answer 21

neither

Answer 22

that derivative is not quite right

Answer 23

http://www.wolframalpha.com/input/?i=derivative+of+%28150*%281.65%29%5Et%29

Answer 24

check out the link with the correct derivative as an approximation

Answer 25

150*ln(1.65)*1.65^t

Answer 26

you got it!!!

Answer 27

phew, that wasn't too bad now, was it ;)?

Answer 28

no, not too bad... but that wasn't the answer lol and neither is 75.1163, which I assumed would be the answer bc I plugged in t for 1...

Answer 29

I GOT THE ANSWER!!!

Answer 30

YAY :)

Answer 31

it was the derivative above... I just plugged it in wrong lol whoops...