Model the data using an exponential function f(x) = Ab^x.
x ,0 ,1 ,2
f(x) ,800 ,480 ,288
Like 800-480=320 and 480-288=192
How do I find the exponential form?
Thank you.
To find the exponential form of the given data, we need to identify the values of A and b in the function f(x) = Ab^x.
From the given data:
x = 0, f(x) = 800
x = 1, f(x) = 480
x = 2, f(x) = 288
Let's use these values to find A and b:
Step 1: Substitute the values of f(x) and x into the function to form equations:
800 = Ab^0
480 = Ab^1
288 = Ab^2
Step 2: Simplify the equations:
800 = A * 1 (since any number raised to the power of 0 is 1)
480 = Ab
288 = Ab^2
Step 3: Solve the equations to find A and b:
From equation 2, we can find A in terms of b:
A = 480/b
Substitute this value of A into equation 3:
288 = (480/b) * b^2
Step 4: Further simplify the equation:
288 = 480b
Divide both sides of the equation by 480:
b = 288/480 = 0.6
Substitute this value of b into equation 2 to find A:
480 = A * 0.6
A = 480/0.6 = 800
Step 5: Write the exponential form:
The exponential form of the given data is:
f(x) = 800 * 0.6^x
To find the exponential form of the data, you need to determine the values of A and b in the equation f(x) = Ab^x, where A is the initial value and b is the base of the exponent.
Let's use the given data points to solve for A and b:
Data Point 1: (x=0, f(x)=800)
Substituting these values into the exponential equation gives: 800 = Ab^0
Simplifying the exponent (anything raised to the power of 0 is 1), we have: 800 = A
Data Point 2: (x=1, f(x)=480)
Substituting these values into the exponential equation gives: 480 = Ab^1
Since A is 800 (from the first data point), we have: 480 = 800b
Dividing both sides of the equation by 800, we get: b = 0.6
Now we have determined the values of A and b. The exponential form of the given data is f(x) = 800 * 0.6^x.