Question

The question is which of the following functions best represents the graphA.)y=0.5x+2.5B.)y=0.5(2.5)^xC.)y=0.5(6)^xD.)y=3.5x^2+0.5

Answer 1

The general form of an exponential function is given below:

$\begin{gathered} y=a(b^x)\ldots.eqn(1) \\ \text{For point (0,0.5), x=0 and y =0.5} \\ \text{substituting the above values into the equation, we get} \end{gathered}$$\begin{gathered} 0.5=a(b^0) \\ 0.5=a(1) \\ a=0.5 \end{gathered}$

For point (1,3); x = 1 and y = 3,

Substituting the above values into the equation, we get

$\begin{gathered} 3=a(b^1) \\ \text{But a=0.5 , so we get} \\ 3=0.5(b) \\ 3=\frac{1}{2}b \\ \text{Cross multiplying, we get} \\ b=3\times2 \\ b=6 \\ So,\text{ the exponential equation becomes} \\ y=0.5(6)^x \end{gathered}$

Thus, the correct answer is y = 0.5(6)^x (option C)