Exponential Growth?

Question

A painting, purchased for $10 000 in 1990, increased in value by 8% per year. Find the value of the painting in the year 2000.

Answer 1

The general function is:
P(t) = Po * e^(t * ln(1+r))
where P(t) is the price/value after t units of time (years in this case), Po is the initial price/value ($10,000), and r is the rate (.08 here).
Substitute the numbers you have and solve:
2000-1990 = 10, so t = 10
P(10) = 10,000 * e^(10 * ln(1 + .08))
P(10) = 21,589.25
So after 10 years, the painting will be worth $21,589.25

Answer 2

A=P(1+r/100)^n
A=10000(1.08)^10

Answer 3

1990 = 0 (starts out)
2000 = 10 (10 years later)
A(t) = P(1+r)^t
So...

A(10) = initial (1+interest)^time
A(10) = 10,000 (1+0.08)^10
A(10) = 10,000 (1.08)^10
A(10) = 21589.25
After 10 years the painting is worth $21,589.25
You don't use e beacause the value is not growing continually. It is per year.

Answer 4

exponential growth = e^(rate * time)
e^(8% * 10) = e(.8) = 2.225540928

10 000 * 2.225540928 = 22 255.40928

Answer 5

uh, why not just use the exponential growth formula? this explains it step-by-step.

http://math.usask.ca/emr/examples/expgrtheg.html

hope that explains it well enough for you.