I NEED HELP PLEASE, THANKS! :) Astronomers classify stars according to their brightness by assigning them a stellar “magnitude.” The higher the magnitude the dimmer the star. The dimmest stars visible to the naked eye have stellar magnitudes of 6. The table below shows the relative brightness of different stellar magnitudes.
a. Find an equation that gives the relative brightness in terms of stellar magnitude.
b. Use this equation to find the relative brightness of a star with magnitude 9.
(SHOW WORK)

 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

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

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116