Question

Change the function, y=3(0.5)^x,to a function with base e

Answer 1

y=3e^(ln0.5)x

Step-by-step explanation:

Answer 2

y = 3(e)^(-0.69x)

Step-by-step explanation:

Taking into account the following property

`a=e^(\ln a)`

We can replace (0.5)^x by

`\begin{gathered} 0.5^x=e^{\ln \text{ (0.5\textasciicircum{}x)}} \\ 0.5^x=e^(x\ln (0.5)) \end{gathered}`

So, now we can rewrite the function as

`\begin{gathered} y=3e^(x\ln (0.5)) \\ y=3e^(x(-0.69)) \\ y=3e^(-0.69x) \end{gathered}`

Therefore, the answer is

y = 3(e)^(-0.69x)