Exponential Functions, Please Help!!

[NovaDragon]

I can't seem to make an equation that satisfies the last condition.

I know that the first 3 tell me

It's translated up 5 units
reflected across x-axis
y-intercept is 4.5


Can someone please help me with the 4th one?

 

[tkhunny]

"Pure" exponential?

\(\displaystyle h(x) = ae^{bx}\)

\(\displaystyle \frac{h(x+1)}{h(x)} = \frac{ae^{b(x+1)}}{ae^{bx}} = \frac{ae^{bx}\cdot e^{b}}{ae^{bx}} = e^{b}\)

 

[NovaDragon]

So the function has a base of "e"?

Also |f(x+1)/f(x)|=5

 

[tkhunny]

Just an example.

\(\displaystyle \frac{h(x+1)}{h(x)} = \frac{aq^{b(x+1)}}{aq^{bx}} = \frac{aq^{bx}\cdot q^{b}}{aq^{bx}} = q^{b}\)

There are some restrictions on q, but not as many as you may be imagining.