Question

Determine the exponential equation for the graph below. If a value is non-integer type is as a fraction:as x goes to negative infinity f(x) approaches 7. Y intercept of (0,5). as x goes to infinity f(x) goes to negative infinityThe coefficient is AnswerThe base is AnswerThe exponent on our transformed function is AnswerThe constant we are adding to our function is Answer

Answer 1

The general form of an exponential function is

`y=a(b)^x+c`

The graph of the function is inverted and shifted by 7 units to give

`y=-a(b)^x+7`

Where

`x=0,y=5`

Substitute for x and y in the general form of an exponential function

`\begin{gathered} y=-a(b)^x+7 \\ 5=-a(b)^0+7 \\ 5=-a(1)+7 \\ 5=-a+7 \\ \text{Collect like terms} \\ a=7-5 \\ a=2 \end{gathered}`

Where x = 1, y = 0.5, substitute into the function

`\begin{gathered} y=-a(b)^x+7 \\ 0.5=-2(b)^1+7 \\ 0.5=-2b+7 \\ \text{Collect like terms} \\ 2b=7-0.5 \\ 2b=6.5 \\ \text{Divide both sides by 2} \\ (2b)/(2)=(6.5)/(2) \\ b=(13)/(4) \end{gathered}`

The exponential function is

`y=-2((13)/(4))^x+7`

Hence,

The coefficient, a, is -2.

The base is, b, 13/4

The exponent is x

The constant, c, we adding to our function is 7