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

0.07947

Step-by-step 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:

`(d(a^x))/(dx)=a^x\log a`

`(d(P))/(dt)=(d(1.05)^t)/(dt)=1.05^t\ln (1.05)`

`(d(P))/(dt)=(d(1.05)^(10))/(dt)=1.05^(10)\ln (1.05)`

After solving this, the value is 0.07947