write the exponential function f(x)=-3*4^(1-x) in the form f(x)=ab^x
a. f(x)=-12*(-4)^x
b. f(x)=-12*(-1/12)^x
c. f(x)=-12*(1/4)^x
d. f(x)=-3*(1/4)^x
d. f(x)=-3*(1/4)^x
c.
f(x)=-3*(1/4)^x
the answer is c. f(x)=-12*(1/4)^x
I apologize for the earlier incorrect response. You are correct, the exponential function f(x)=-3*4^(1-x) can be written as f(x)=-12*(1/4)^x.
the answer is c. f(x)=-12*(1/4)^x show all of the steps
Apologies for the confusion. Here are the steps to rewrite the exponential function f(x) = -3*4^(1-x) in the form f(x) = ab^x:
1. Start with f(x) = -3*4^(1-x).
2. Use the property of exponents that says a^(b-c) can be written as (a^b)/(a^c).
3. Rewrite 4 as (2^2) because 4 is equal to 2 raised to the power of 2.
4. Substitute this into the equation: f(x) = -3*(2^2)^(1-x).
5. Use the property of exponents to simplify further: f(x) = -3*(2^(2(1-x))).
6. Simplify the exponent: 2(1-x) = 2 - 2x.
7. Substitute the simplified exponent back into the equation: f(x) = -3*2^(2-2x).
8. Use the property of exponents that says a^(b+c) can be written as (a^b)*(a^c).
9. Apply this property to further simplify: f(x) = -3*(2^2)*(2^(-2x)).
10. Evaluate 2^2 = 4 and 2^(-2x) = (1/4)^x to get the final form:
f(x) = -12*(1/4)^x.
Therefore, the exponential function f(x) = -3*4^(1-x) can be written in the form f(x) = -12*(1/4)^x.