An original signature of supermodel Jill Fisher appreciates in value 7% every year. How much was it worth in 2000 if it is worth $80,000 in 2016?
This is about exponential growth and decay problem. thank you
x(1.07)^16 = 80000
solve for x, the original value
so the answer will be 72,429?
or will be 4,673?
Will be 27,099
yes, your last one of $27,099 is correct
To solve this exponential growth problem, we will use the formula for exponential growth:
A = P(1 + r)^t
Where:
A is the final amount
P is the initial amount (the value in 2000)
r is the growth rate per time period (7% or 0.07)
t is the number of time periods (16 years from 2000 to 2016)
We are given that the final amount (A) is $80,000 and we need to find the initial amount (P).
Plugging in these values into the formula, we get:
$80,000 = P(1 + 0.07)^16
To find the initial amount (P), we need to isolate it. Divide both sides of the equation by (1 + 0.07)^16:
P = $80,000 / (1 + 0.07)^16
Calculating this expression, we find that P is approximately $34,964.96.
Therefore, the original signature of supermodel Jill Fisher was worth approximately $34,964.96 in 2000.