Function f is an exponential function.x βˆ’4 βˆ’2 0 2 4f(x) 316 34 3 12 48By what factor does the output value increase as each input value increases by 1?

Accepted Solution

Answer:The output value increased by factor 2.Step-by-step explanation:The general form of the exponential function is[tex]f(x)=ab^x[/tex]Where, a is initial value and b is growth factor.From the given table it is noticed that at x=0, the value of f(x) is 3. It means the initial value is 3.[tex]a=3[/tex]The another value of f(x) is 12 at x=2.[tex]f(3)=ab^2[/tex][tex]12=(3)b^2[/tex][tex]4=b^2[/tex][tex]b=2[/tex]The required function is [tex]f(x)=3(2)^x[/tex]Since the growth factor is 2, therefore the output value increased by factor 2.