With a yearly rate of 3 percent, prices are described as P = Po(1.03)^t, where Po is the price in dollars when

Question

t = 0 and t is time in years. If Po is 1.2, how fast are prices rising when t = 15?

Answer 1

P=1.2(1.03)^t

Since you want to know how fast, you are talking about the derivative.

P'=1.2 * ln(1.03) * (1.03)^t

Because the derivative of a^t is ln(a) * a^t where a is the base and t is the variable (this is an exponential function).

Plug in 15, you get:

P'=1.2 * ln(1.03) * (1.03)^15=0.05526 dollars/year (positive so it's increasing)

Answer 2

After time t , the prices will still rising at the rate of 3% pa, but their level will be

1.2 x (1.03)6^15 = 1.870

Answer 3

P15
=1.2[1.03]^15
=1.2*1.55796
=1.869

Answer 4

Of course, if the question is "how fast" ... "when" ..., you must take the first derivative. Only Maddie's answer could be correct.

Answer 5

P=1,2 * (1,03)^15
TAKE LOG OF BOTH SIDES

log P=log(1.02)+15*log 1,03

use excel or your calculator to find log P,
then the value of P