# Differential equation for slope

#### 3B1B

##### New member
I have this slope equation where it wants me to find the slope of two points from a function:

What is the slope of the secant line that intersects the graph of f(x) = 32x at x=0, and x=2?

The first thing I don't get is the power to 2x, what does that mean? does it mean power by 2, then by x or all in one go?

other than that, I believe I do know how to do the rest, by finding the difference and then just plugging the values in the slope formula.

Any help is appreciated.

Last edited:

#### skeeter

##### Elite Member
$$\displaystyle m = \frac{f(2)-f(0)}{2-0}$$

• 3B1B

#### AmandasMathHelp

##### New member
You should multiply x by 2 before you take the 3 to a power. The 2x is the exponent on 3.

For example when x=5 you would do $$\displaystyle 3^{2*5}= 3^{10}$$

It is notable that you can actually rewrite this to do the power of 2 first then x, like you said. But that would look more like this. You will get the same answers either way.

$$\displaystyle 3^{2*x} = (3^{2})^x = 9^x$$

• 3B1B

#### 3B1B

##### New member
You should multiply x by 2 before you take the 3 to a power. The 2x is the exponent on 3.

For example when x=5 you would do $$\displaystyle 3^{2*5}= 3^{10}$$

It is notable that you can actually rewrite this to do the power of 2 first then x, like you said. But that would look more like this. You will get the same answers either way.

$$\displaystyle 3^{2*x} = (3^{2})^x = 9^x$$
As AmandasMathHelp said, $$\displaystyle 3^{2x}= (3^2)^x= 9^x$$. For x= 2 that is $$\displaystyle 9^2= 81$$.
You could also do this as $$\displaystyle 3^{2(2)}= 3^4= 3(3)(3)(3)= 9(3)(3)= 27(3)= 81$$.