Convert the given exponential function to the form indicated. Round all coefficients to four significant digits.
f(x) = 9e^3x; f(x) = Ab^x
How do i solve the equation with this formula?
Thanks
12 years ago
1 year ago
To convert the exponential function, f(x) = 9e^3x, to the form f(x) = Ab^x, we need to find the values of A and b.
The general form of an exponential function is f(x) = Ab^x, where A represents the initial value and b represents the growth factor.
To find A and b, we first need to rewrite the given function in the form f(x) = Ab^x. Notice that e is a constant (approximately equal to 2.71828), so we can rewrite the function as:
f(x) = 9 * (e^3)^x
Now, simplify the exponent:
f(x) = 9 * e^(3x)
Comparing this equation with the general form, we can see that A = 9 and b = e^3.
To round all coefficients to four significant digits, round the value of e^3 (which is approximately 20.0855) to four decimal places:
A = 9 (rounded to four significant digits)
b = 20.0855 (rounded to four decimal places)
Therefore, the converted exponential function is f(x) = 9 * 20.0855^x.