Does the rule y=-3(4^x) represent an exponential function?
a. yes
b. no ***
yes, it does. 4^x is an exponential function
The -3 is just a scale factor
To determine whether the rule y = -3(4^x) represents an exponential function, we need to understand the characteristics of an exponential function.
An exponential function is of the form y = a * b^x, where a and b are constants.
In our case, the equation is y = -3(4^x). We can rewrite this equation as y = -3 * (2^2)^x, which simplifies to y = -3 * 2^(2x).
Comparing this equation to the general form of an exponential function, we see that the base, 2, is a constant. However, the exponent, 2x, is not a constant. In an exponential function, the exponent must be a variable (such as x) and not a combination of a variable and a constant.
Based on this analysis, we conclude that the rule y = -3(4^x) does not represent an exponential function. Thus, the correct answer is b. no.