Answer:
An exponential function in the form of y = a(m) x is of the form:
y = a * m^x
where "a" is a constant, "m" is a positive constant (the base of the exponential), and "x" is the independent variable.
To determine the exponential function in this form, you need to have some information about the function, such as its value at a particular point or its rate of growth.
Here are the general steps to determine the exponential function in the form of y = a(m) x:
Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.
Determine the value of "m" by solving for it using the given information.
For example, let's say you are given that the function passes through the point (2, 8) and has a growth rate of 3. To determine the exponential function in the form of y = a(m) x, you would follow these steps:
Plug in the values of x and y into the equation:
8 = a * m^2
Solve for "a" by isolating it on one side of the equation:
a = 8 / m^2
Use the given growth rate of 3 to find the value of "m":
m = 1 + r = 1 + 0.03 = 1.03
Plug in the value of "m" and the value of "a" you found in step 2 into the equation:
y = (8 / 1.03^2) * 1.03^x
Simplifying this equation gives:
y = 7.514 * 1.03^x
So the exponential function in the form of y = a(m) x that passes through the point (2, 8) and has a growth rate of 3 is y = 7.514 * 1.03^x.
Explanation:
here is a more detailed explanation of the steps involved in determining an exponential function in the form of y = a(m) x:
Determine the value of "a" by plugging in the known value of "y" and "x" into the equation.
In the equation y = a(m) x, "a" is a constant that represents the value of y when x is equal to 0. So to find the value of "a", we need to know the value of y for a specific value of x, other than 0.