BUS 111 Lecture Notes - Lecture 1: Reverse Engineering
Document Summary
This type of function is useful in modeling population growth, inflation, and learning curves. Def- an exponential function is on of the form of f(x)= ax and a>0 and a 1. Note- exponentials all look the same (pretty much), they have no x-intercepts. (you can never plug in a 0 and get a 0). Sometimes, we want to reverse engineer the exponential. E is what happens to this quantity (1+1/x)x as x gets really really large. (1+1/100)100 =2. 70401 (1+1/1000)1000 =2. 71692. Application example-suppose the price of a gallon of gasoline is 2. 19 at an average inflation rate of 3. 6%. Solution- note tat inflation is a continuous process that can be modeled by f(x)=aert. Where f= future value, a is the starting amount, r= rate and t= time. Def- for a>0, a 1, we define the logarithm base a as log s(x)=y meaning that ay=x. We know that ? should be 3, so we would write log4(64)=3.
