Question

Can Someone help me and show their work on how they got it!

Answer 1

Answer: y = 160*(1/2)^x

Note: we can write this as y = 160*(0.5)^x which is the decimal form equivalent

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Explanation:

Focus on the y column. Notice how the values are cut in half each time. So this means b = 1/2 where the general form is y = a*b^x

The initial value is a = 160 because we go in reverse of taking half to multiply the 80 by 2 to get 80*2 = 160. So when x = 0, y = 160. Then we can check to see that taking half of 160 does in fact lead to 80.

So with a = 160 and b = 1/2 = 0.5,
this means the equation is either y = 160*(1/2)^x or y = 160*(0.5)^x 

The two represent the same basic idea.

As a check, let's plug in x = 1 and we get
y = 160*(1/2)^x
y = 160*(1/2)^1
y = 160*0.5
y = 80
So if x = 1 then y = 80 which confirms the first row of the table.

I'll let you check the other rows of the table as practice.