SOLUTION: Suppose that the value of a certain antique collection increases with age and its rate of appreciation at any time is proportional to its value at that time. If the value of th

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Question 1150408: Suppose that the value of a certain antique collection increases with age and
its rate of appreciation at any time is proportional to its value at that time.
If the value of the collection was Php 25,000 10 years ago and its present value
is Php 35,000, in how many years is its value expected to be Php50,000?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that the value of a certain antique collection increases with age and
its rate of appreciation at any time is proportional to its value at that time.
If the value of the collection was Php 25,000 10 years ago and its present value
is Php 35,000, in how many years is its value expected to be Php50,000?



Edwin

Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The phrase "its rate of appreciation at any time is proportional to its value at that time" means this is exponential growth.

The basic formula for exponential growth is

y+=+a%28b%5Ex%29

a is the initial value and b is the (annual) growth factor.

The current value is 35,000.

The growth factor over 10 years is 35000%2F25000+=+7%2F5+=+1.4; the annual growth factor is %281.4%29%5E%281%2F10%29.

The number of years it will take the value to increase to 50,000 is found by solving the equation

35000%281.4%29%5E%28%281%2F10%29%5Ex%29+=+35000%281.4%29%5E%28x%2F10%29+=+50000

Graphing the expressions on both sides of the equation on a graphing calculator shows the solution to be 10.6 years.