Sudharaka said:Jordan from Facebook writes:
Got the first one right, don't know exactly what it's asking for in the 2nd part(I missed the class that we went over these types of problems) thanks!
An exponential function is a mathematical function of the form f(x) = ab^x, where a and b are constants and x is the independent variable. The value of b is known as the base and determines the rate at which the function increases or decreases.
To graph an exponential function, plot a few points by choosing values for x and calculating the corresponding values for y using the function. Then, connect the points with a smooth curve. It is important to note that the curve of an exponential function never touches the y-axis, but gets closer to it as x approaches negative infinity.
An exponential function has a variable in the exponent, while a linear function has a variable in the coefficient. In other words, the rate of change in an exponential function increases or decreases exponentially, while the rate of change in a linear function is constant.
Exponential functions are used to model situations that involve growth or decay over time. Some real-life examples include population growth, radioactive decay, and compound interest.
The inverse of an exponential function is a logarithmic function. In other words, if f(x) = ab^x is an exponential function, then its inverse is given by f^-1(x) = log base b (x/a). This means that the input and output values of the original function are reversed in the inverse function.