MHF4U
Culminating Activity
Rates of Change In Career
EXPONENTIAL & LOGARITHMIC FUNCTION
EXPONENTIAL FUNCTION
LOGARITHMIC FUNCTION
In the exponential function,there are two ways to figure out the function. the genal formula is f(x)=a(m)^x (m>0). If the m is greater than 1, the function is increasing like left picture. On the other hand, the m is less than 0, the function is decaying. If the function is increasing, the rate of changof the exponential function gets bigger and
bigger. This means the function goes up faster and faster. On the other hand, the function is decaying, the y-value of the function goes down to closely 0 slower and slower.
Therfore, the rate of change is ot constant, and then the increasing exponential function shows the line of the graph gets steeper and steeper. Therefore, the function's shape is smooth curve. On the other hand, the decaying function goes smaller slower and slower Consequently, the function's shape is curved.
The logarithmic functionis the inversed function. The base of logarithm cannot be negative according to the exponential function. When the base is greater than 1, the function is increasing forever. On the other hands, when the base is less than 1, the function is decaying. When the base is greater than 1, and the rates of change is decreased more and more. On the
other hand,b when the base is less than 1, te function is decayin, and the rates of change is also decaying more and more.
Therefore, the shapes of the functions in this year are both curved. Also, when the increasing logarithm function that the base is greater than 1. After that, the line gets more and more flat while curving. On the other hand, when the decaying logarithmic function that the base is smaller than 1 . the line goes down and gets negative.
ECONOMISTS
The economist is the reseacher of the economy in the country. The people in this career use a lot of real world data to find the way to create the bettter economy. They often see the condition of the stock market since they can compare their own country with others. As a resulthe purpose of economist is to find the reasons why the successful company gets better and spread its system to others to create better society. The GDP is related in the exponential function because nowadays, all country growths faster and faster each year to be success. Furthermore, they observe change of rate of change to show us how the growth of the country is stopped or improved, and then look for the solution the economy in the world gets better.
APPLICATION QUESTIONS
In the current world,a lot of country grows up so quickly, and then nowadays, United States of America and Russia causes the conflicts to get the highest positioin the world. During this time, China grows up quickly to catch up to them and keeps growing up until now. Lastar, China's GDP is represented by
Determine the averge rate of change between x=7 and x=8.
