Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

Answer:  a) y = 250(0.4)ˣ

                b) 0.065536

Step-by-step explanation:

Create a system of equations in the form y = a(b)ˣ

• where y is the Relative Brightness
• x is the Stellar Magnitude

$Equation\ 1: 100=a(b)^1\\Equation\ 2: 40=a(b)^2\\\\\\\text{Set each equation equal to a to solve for b:}\\Equation\ 1: \dfrac{100}{b}=a\qquad Equation\ 2: \dfrac{40}{b^2}=a\\\\\\\dfrac{100}{b}=\dfrac{40}{b^2}\\\\\\100b^2=40b\\\\0.4=b$

Now insert b = 0.4 into one of the equations to solve for "a":

$100=a(0.4)^1\\\\\\\dfrac{100}{0.4}=a\\\\\\\dfrac{1000}{4}=a\\\\\\250=a$

Now we have our equation for part (a) y = 250(0.4)ˣ

For part (b), replace the x with 9 and solve.

y = 250(0.4)⁹

 = 0.065536

Answer 2

Answer:

a. y = 250 (0.4)^x

b. 0.066

Step-by-step explanation:

The equation can be modeled as a geometric sequence, where the first term is 100 and the common ratio is 0.4.

y = 100 (0.4)^(x − 1)

This can also be simplified to:

y = 250 (0.4)^x

When x = 9:

y = 250 (0.4)^9

y = 0.066