How fast is the price decreasing, in hundreds of dollars, at the beginning of year 1?

Question

In the past two decades, the price of some hardware has decreased logarithmically. For a certain brand of hardware, the price, in hundreds of dollars, is modelled by the following function: 

f(x)=−2 log2x+8

where x is number of years. For example, the price in year 1 is $800

Answer 1

To find the rate of change of the function, you need the derivative:

d/dx(2log2x +8) = 4/(2x) where I have assumed that you meant natural log. If you actually meant log₁₀, then you should transform the equation using log₁₀x = lnx/ln(10) before you take the derivative.

Plug in 1 for x , i.e. evaluate f'(1) and multiply by 100 to get $/yr