Question

Find the missing values for the exponential function represented by the table below. x values: 0, 1, 2, 3, 4 y values: 24, 40.8, 69.36, _____, _____

Answer 1

$f(x)=b(a)^x\\\\x=0\to y=24\qquad\text{substitute}\\\\b(a)^0=24\to b=24\\\\x=1\to y=40.8\qquad\text{substitute}\\\\24(a)^1=40.8\qquad\text{divide both sides by 24}\\\\a=1.7\\\\f(x)=24(1.7)^x\\\\\text{check for x = 2}\\\\f(2)=24(1.7)^2=24(2.89)=69.36\qquad\text{CORRECT}\\\\f(3)=24(1.7)^3=24(4.913)=117.912\\\\f(4)=24(1.7)^4=24(8.3521)=200.4504$