Just one step away. Exponential formula

Question

The data points are.

I have worked out that.

y =.032(2.5)^x is correct where my table is

x = 0, y = .032

x = 1, y = .08

x = 2, y = .2

How do I get my formula to reflect y=-3, x =.0320 ect..

Answer 1

Hint: Currently, you have it so that you get the value you want at $-3$ when $x=0$, and the value you want at $-2$ when $x=1$, and so on. Therefore, you want have an $x$ which is $3$ larger than it should be. How should you change your equation to reflect this?

Response to the comments: One of the subtleties in PEMDAS/BEDMAS is that certain things are secretly parentheses: $y=0.32(2.5)^{x-3}$ "really" means $y=0.32(2.5)^{(x-3)}$. Other things that do this include

• fractions: $\frac{a+b}{c+d}$ is the same as $\frac{(a+b)}{(c+d)}$
• square roots: $\sqrt{x+y}$ is the same as $\sqrt{(x+y)}$
• Sometimes, composition of functions. No examples, because if you've seen it you've seen it and if not it'll just be confusing.