Question 8

Find the exponential function $f (x) = C a^{x}$ whose graph goes through the points $(0; 2)$ and $(2, 8)$ .
$\begin{array}{l} a = \\ C = \end{array}$
Question Help:
Message instructor

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $a = 2, C = 2$

Steps

Step 1 ：Let's denote the exponential function as $f (x) = C a^{x}$ . We know that the graph of this function goes through the points (0 ; 2) and (2,8).

Step 2 ：Substituting the point (0 ; 2) into the function, we get $f (0) = C a^{0} = C = 2$ . So, $C = 2$ .

Step 3 ：Substituting the point (2,8) into the function, we get $f (2) = C a^{2} = 2 a^{2} = 8$ .

Step 4 ：Solving the equation $2 a^{2} = 8$ for $a$ , we get two possible solutions, $a = - 2$ and $a = 2$ .

Step 5 ：However, in the context of an exponential function, $a$ should be positive. Therefore, we discard -2 and take $a = 2$ .

Step 6 ：Final Answer: $a = 2, C = 2$

Question 8 Find the exponential function f(x)=Cax whose graph goes through the points (0;2) and (2,8).a=C=Question Help:Message instructor

Answer

Popular Problems

Question 8

Find the exponential function $f (x) = C a^{x}$ whose graph goes through the points $(0; 2)$ and $(2, 8)$ .
$\begin{array}{l} a = \\ C = \end{array}$
Question Help:
Message instructor