Help me with this please please

Step-by-step explanation:

Actually, the lesson is giving you wrong information. The exponential function written in the example does not work for the point (4, 24).

Here's another way to look at it.

Given

  two points: (x1, y1) and (x2, y2)

Solution

The exponential function can be written as ...

  y = (y1)(y2/y1)^((x -x1)/(x2 -x1))

Example

For the example points, the function would be ...

  y = (6)(24/6)^((x-2)/(4-2)) = 6·4^(x/2 -1) = (6/4)(4^(1/2))^x = (3/2)2^x

Check

  For x=2, y=(3/2)2^2 = 6. For x=4, y = (3/2)2^4 = 24.

You will notice that we figure out "b" and "a" as a part of the process of simplifying the equation. The equation would work perfectly well without simplification.

1. Given points (2, 50) and (3, 250), the equation is ...

  f(x) = 50(250/50)^((x -2)/(3 -2)) = 50·5^(x -2) = (50/25)5^x

  f(x) = 2·5^x . . . b = 5; a = 2

__

2. Given points (1, 3) and (2, 9/2), the equation is ...

  f(x) = (3)(3/(9/2))^((x -1)/(2 -1)) = (3)(2/3)^(x -1) = (3/(2/3))(2/3)^x

  f(x) = (9/2)(2/3)^x . . . b = 2/3; a = 9/2

__

3. Given points (3, 32) and (4, 128), the equation is ...

  f(x) = (32)(128/32)^((x -3)/(4 -3)) = (32)4^(x -3) = (32/64)4^x

  f(x) = (1/2)4^x . . . b = 4; a = 1/2

Additional comments

The usual rules of exponents are useful in this:

  a^(b+c) = (a^b)(a^c)

  a^(bc) = (a^b)^c

  a^-b = 1/a^b

i dont get the question

step-by-step explanation: