Question

With yearly inflation of 5%, prices are given by P=P0(1.05)t, where P0 is the price in dollars when t=0 and t is time in years. Suppose P0=1. How fast (in cents/year) are prices rising when t=10? Round your answer to two decimal places.

Answer 1

Answer:

0.07947

Explanation:

Given that

P=P0(1.05)t

where

P0 represents the price in dollars

Plus P0 = 1  

T = time = 10 years

So the equation is

P = 1(1.05)^10

The formula is shown below:

$\frac{d(a^x)}{dx}=a^x\log a$

$\frac{d(P)}{dt}=\frac{d(1.05)^t}{dt}=1.05^t\ln (1.05)$

$\frac{d(P)}{dt}=\frac{d(1.05)^{10}}{dt}=1.05^{10}\ln (1.05)$

After solving this, the value is 0.07947