Question

A sculpture was purchased for $4,000. The value of the sculpture increases at a rate of 4% per year.

How much will the sculpture be worth after 10 years?

Answer 1

5600

Answer 2

A = 4000(1.04)^10 assuming annual increases

A = 4000exp(0.40) assuming continuous increase

Answer 3

You would multiply 4 by 10 and get 40 % then use a calculator and put in 4000 + 40% and get 5600

Answer 4

Wait... so which is it :/

Answer 5

@douglaswinslowcooper what would i do next to find the answer?

Answer 6

"4% per year" indicates compounding yearly, usually

final value = 4000 (1.04)^10 = 5921

Answer 7

Thank you! So now it is asking:In how many years will the sculpture be worth $10,000? Round to the nearest tenth of a year.
Would i then do 10,000(1.04)^t

Answer 8

10000 = 4000(1.04)^n solve for n
take logarithms

10000/4000=2.5
log(2.5) = n log(1.04)

n = log(2.5)/log(1.04) = 23.4 years

check: : (1.04)^23.4 = 2.5 checks

Answer 9

Thank you so much!!

Answer 10

You are very welcome.