find the base of the exponential function whose graph contains the given points.
1.( 4, 1/625)
2.(3/2, 27)
3.(3, 1/343)
Help needed!
Find the base of the exponential function whose graph contains the given points.
1. (2,16)
2. (1,10)
3. (3,64)
4. (3,1/343)
5. (4,1/625)
6. (3/2,27)
I'll do #1. You can try the others.
625 = 5^4, so f(x) = 1/5^x or 5^-x
thanks.. :)
1. Well, to be honest, that base is pretty shy. It's hiding behind a little fraction, making it hard to see. But don't worry, I'll reveal it to you! The base of the exponential function is 1/5.
2. Ah, there you are, base! It seems you want to show off a bit. The exponential function's base is 2/3. Just remember, don't let that base give you a big head!
3. Whoa, talk about being a tiny base! The exponential function's base here is 1/7. It's so small, you might need a microscope to see it. Good luck finding it in an exponential crowd!
To find the base of an exponential function whose graph contains the given points, you can use the general form of an exponential function: f(x) = a * b^x, where a is a constant and b is the base of the exponential function.
Let's use the given information to solve for the base (b) in each case:
1. For the point (4, 1/625), we can substitute the x and y values into the exponential function equation:
1/625 = a * b^4
Since b is the base, we can rewrite this equation as:
b^4 = 1/625
To solve for b, take the fourth root of both sides:
b = (1/625)^(1/4)
2. For the point (3/2, 27), we have the equation:
27 = a * b^(3/2)
To solve for b, rewrite the equation as:
b^(3/2) = 27
Raise both sides to the power of (2/3):
b = 27^(2/3)
3. For the point (3, 1/343), we get:
1/343 = a * b^3
Rewriting the equation as:
b^3 = 1/343
To solve for b, take the cube root of both sides:
b = (1/343)^(1/3)
By following these steps, you can find the base (b) of the exponential function whose graph contains the given points.