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

Question

asked Feb 2, 2023 113k views

2 Answers

Gerson Dantas · Answer 1 · 2023-02-08T14:06:56+0000

Answer:

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)