Calculus Problem: Rate of Change in Minecraft FPS

Question

A Minecraft player notices improved game performance after installing OptiFine. Before using OptiFine, their frame rate (FPS) is modeled by the function:

f(t)=60+10ln⁡(t+1)f(t) = 60 + 10\ln(t + 1)f(t)=60+10ln(t+1)After installing OptiFine, the FPS is modeled by:

g(t)=90+15ln⁡(t+1)g(t) = 90 + 15\ln(t + 1)g(t)=90+15ln(t+1)where ttt is the time in minutes since the game started.

Question:

1. What is the instantaneous rate of change of FPS at t=4t = 4t=4 minutes for both models?
2. How much more responsive is the FPS after installing Optifine at that moment?

Answer 1

1) Take the derivatives of f(t) and g(t). Then find f'(4) and g'(4).

The units will be frames/s²

2) Find g'(4) - f'(4).