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Video transcript

G is an exponential function with an initial value of negative 2 so an initial value of negative 2 and a common ratio of 1/7 common ratio of 1/7 write the formula for G of T well the fact that it's an exponential function we know that it's formula is going to be of the form G of T is equal to our initial value which we could call a times our common ratio which we could call R to the T power it's going to have that form and they tell us what the initial value is it's negative 2 so this right over here is negative 2 and we know that the common ratio is 1/7 so this is 1/7 so let me just write it again a little bit neater G of T is going to be equal to our initial value negative 2 times times our common ratio 1/7 to the T power and hopefully this makes sense initial value is this number well if T is equal to 0 then 1 7 to the 0 power is 1 and so G of 0 you can view that at time is being equal to 0 if you view T as time would be equal to negative 2 so that would be our initial value and then if you think about every time you increase T by 1 you're going to you're going to multiply by 1/7 again and so the ratio between successive terms is going to be 1/7 and so that's why we call that the common ratio hopefully you found that interesting