The exponential function f(x)=6(4)^2x+2 can be written in the standard form f(x)=Abx. Find the values of A and b. Give exact values, not decimal approximations.
I don't know how to do with this problem. I try to graph and use points but the answer is wrong
I can not figure out what you mean.
y = 6 * 4^2x + 2
or
y = 6 * 4^(2x + 2)
or
y = 6 * 4^2 * x + 2
or
y = 6 * 4^2 * (x + 2)
and none of the above ca be expressed as y = A b x as far as I know
To write the exponential function f(x) = 6(4)^(2x+2) in the standard form f(x) = Ab^x, we need to express it as a product of a coefficient A and a base b raised to the power of x.
We start by factoring out the base. In this case, the base is 4. Therefore, we can rewrite the function as:
f(x) = 6 * (4^2)^x * 4^2
Next, we simplify the exponent of the first term. The property of exponents states that (a^b)^c = a^(b*c). Applying this property to the first term, we have:
f(x) = 6 * 4^(2x + 4)
Now, we can see that the base of the exponent is 4, and the coefficient is 6. Therefore, A = 6 and b = 4.
Hence, the values of A and b in the standard form f(x) = Ab^x for the given exponential function are A = 6 and b = 4.