which equation represents an exponential function that passes through the point (2, 36)?\n$f(x)=4(3)^x$\n$f(x…
which equation represents an exponential function that passes through the point (2, 36)?\n$f(x)=4(3)^x$\n$f(x)=4(x)^3$\n$f(x)=6(3)^x$\n$f(x)=6(x)^3$
Answer
Explanation:
Step1: Recall exponential - function form
An exponential function is of the form (y = a(b)^x). We need to check each option by substituting (x = 2) and (y=f(x)=36).
Step2: Check option (f(x)=4(3)^x)
Substitute (x = 2) into (f(x)=4(3)^x). Then (f(2)=4\times(3)^2=4\times9 = 36).
Step3: Check option (f(x)=4(x)^3)
This is a power - function, not an exponential function. But if we substitute (x = 2), (f(2)=4\times(2)^3=4\times8 = 32\neq36).
Step4: Check option (f(x)=6(3)^x)
Substitute (x = 2) into (f(x)=6(3)^x). Then (f(2)=6\times(3)^2=6\times9 = 54\neq36).
Step5: Check option (f(x)=6(x)^3)
This is a power - function, not an exponential function. And if we substitute (x = 2), (f(2)=6\times(2)^3=6\times8 = 48\neq36).
Answer:
A. (f(x)=4(3)^x)