I'm sorry, I don't have much. I have the same problem. The answer I have so far is they are alike because they both have to have a constant rate as they increase. You can't change the slope or the exponent after going up a graph while graphing.
is the relationship linear or exponential
There are no points of discontinuity for exponential functions since the domain of the general exponential function consists of all real values!
You find out if a problem is linear or exponential by looking at the degree or the highest power; if the degree or the highest power is 1 or 0, the equation is linear. But if the degree is higher than 1 or lower than 0, the equation is exponential.
All linear equations are functions but not all functions are linear equations.
The linear function changes by an amount which is directly proportional to the size of the interval. The exponential changes by an amount which is proportional to the area underneath the curve. In the latter case, the change is approximately equal to the size of the interval multiplied by the average value of the function over the interval.
They have infinite domains and are monotonic.
Linear equations are a small minority of functions.
is the relationship linear or exponential
Piecewise, linear, exponential, quadratic, Onto, cubic, polynomial and absolute value.
Exponential Decay. hope this will help :)
neither linear nor exponential functions have stationary points, meaning their gradients are either always +ve or -ve
They are similar because the population increases over time in both cases, and also because you are using a mathematical model for a real-world process. They are different because exponential growth can get dramatically big and bigger after a fairly short time. Linear growth keeps going up the same amount each time. Exponential growth goes up by more each time, depending on what the amount (population) is at that time. Linear growth can start off bigger than exponential growth, but exponential growth will always win out.
Exponential and logarithmic functions are inverses of each other.
There are no points of discontinuity for exponential functions since the domain of the general exponential function consists of all real values!
You find out if a problem is linear or exponential by looking at the degree or the highest power; if the degree or the highest power is 1 or 0, the equation is linear. But if the degree is higher than 1 or lower than 0, the equation is exponential.
All linear equations are functions but not all functions are linear equations.
The linear function changes by an amount which is directly proportional to the size of the interval. The exponential changes by an amount which is proportional to the area underneath the curve. In the latter case, the change is approximately equal to the size of the interval multiplied by the average value of the function over the interval.