Question

`k(x) = 3(2) {}^(x) - 8`determine the x intercept and y intercept

Answer 1

Step-by-step explanation:

`\begin{gathered} Given: \\ k(x)\text{ = 3\lparen2\rparen}^x\text{ - 8} \\ We\text{ need to find the x and y intercept} \end{gathered}`

x-intercept is the value of x when the function is equal to zero.

To get the x-intercept we will substitute k(x) with zero and solve for x:

`\begin{gathered} 0\text{ = 3\lparen2}^x)\text{ - 8} \\ 8\text{ = 3\lparen2}^x) \\ divide\text{ both sides by 3:} \\ (8)/(3)=\text{ 2}^x \\ take\text{ log of both sides:} \\ log((8)/(3))\text{ = log2}^x \end{gathered}`
`\begin{gathered} log((8)/(3))\text{ = xlog2} \\ divide\text{ both sides by log2:} \\ x\text{ = }(log((8)/(3)))/(log2) \\ x\text{ = 1.42} \end{gathered}`