Is exponential function similar to Linear function? To figure this out we need to learn about it in detail, so let’s learn what an exponential function is? If you see a smooth graph having exponents, it is an exponential function. It doesn’t have a constant rate of change. Few examples of exponential functions are y = 0.4x.
Here x is the independent variable on which the rate of change depends. So, if the value of x increases the rate of change will also increase and if the value of x decreases the rate of change will also decrease. Unlike linear function, it is not a constant change. The general form of an exponential function is y = (1 + r)^n, where r is the percent change.
You must have heard about linear functions in your higher standards. Though it is a topic that involves graphs but is also easy to understand. Linear in Mathematics means line or a straight line. This line can be found out using a linear function. In short, a graph having a straight line makes a linear function. A linear function looks like this, y = x + 5, where x and y are variables. A linear function keeps changing constantly and the rate of change in a linear function is also called its slope. If the variable x changes, the variable y will change correspondingly making its slope as 1. The typical form of linear function is y = mx +c where the slope or fixed rate of change is denoted by m.
Let’s Learn Few Examples of Linear Functions
- If you’re driving a car at a constant speed, you will notice that the time spent in driving the car and the distance traveled by car in that time is always the same. Here time is an independent variable and distance is a dependent variable.
- If there’s no change in the price of fruits such as bananas, you are likely to be the same no. of bananas you usually buy. Here no. of bananas is independent variable and the total cost is dependent variable.
- If you charge for hourly rates in your job, the relation between the total working hours and the money earned will remain the same. Here the money earned is a dependent variable and the time spent working is an independent variable.
Examples of Exponential Function
- The compound rate doesn’t increase at a fixed rate. It depends on the amount in the account as the amount in your account changes more interest will be added and more interstate will be earned by you so it is not fixed and depends on the balance in the account.
- Another simplest example is that the population of bacteria at a place gets spread faster in an area where the population is more. So if the no. of people is more in an area, then the bacteria will spread fast.
These concepts need to be understood in full detail by solving many related examples. This concept can also be learned live through online tutoring platforms like Cuemath. This will help you to learn it better from Subject matter experts.
Summary of the Topic
Now you know the difference between linear vs exponential growth. If growth is occurring at a constant rate it is called linear growth. For example: if a man is riding in a train and the time spent multiplied by the train speed will give you distance. The distance will either increase or decrease depending on the speed of the train. On the contrary, exponential growth happens at a constant rate.