- #1

Yankel

- 395

- 0

Hello all,

I am trying to solve the following problem:

In the given graph, we see the function:

\[f(x)=ka^{-x} , x\geq 0\]

View attachment 8053

1) Find k and a

2) Find x1

3) Show that an increase of 2 units in x brings a 50% reduction in the value of the function f.

I have tried solving it, but taking two known points from the graph and putting them in the function. I got immediately that:

\[k=8\]

and than less clear, that:

\[a=-\sqrt{2}\]

In the matter of fact, I got two solutions, a solution without the minus sign was there too, but it didn't match the given points...so in order to solve (2), I just guessed and checked my guess.

I am not sure how to show number (3).

Can you kindly verify that my solution is correct and assist with section 3 ? What am I missing with the multiple solutions for a ?

Thank you in advance !

I am trying to solve the following problem:

In the given graph, we see the function:

\[f(x)=ka^{-x} , x\geq 0\]

View attachment 8053

1) Find k and a

2) Find x1

3) Show that an increase of 2 units in x brings a 50% reduction in the value of the function f.

I have tried solving it, but taking two known points from the graph and putting them in the function. I got immediately that:

\[k=8\]

and than less clear, that:

\[a=-\sqrt{2}\]

In the matter of fact, I got two solutions, a solution without the minus sign was there too, but it didn't match the given points...so in order to solve (2), I just guessed and checked my guess.

I am not sure how to show number (3).

Can you kindly verify that my solution is correct and assist with section 3 ? What am I missing with the multiple solutions for a ?

Thank you in advance !