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The balance y (in dollars) of your savings account after t years is represented by y=300(1.05)'. The beginning balance of your friend's account is $340, and the balance increases by $10 each year. a. Compare the account balances by calculating and interpreting the average rates of change from t=2 to t=6.​

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boffeemadrid

Answer:

My balance grows faster than my friends balance.

Step-by-step explanation:

My balance

[tex]y=300(1.05)^t[/tex]

where

t = Time

Average rate from t=2 to t=6 is given by

[tex]\dfrac{t(6)-t(2)}{6-2}\\ =\dfrac{300(1.05)^6-300(1.05)^2}{4}\\ =\mathbf{17.82}[/tex]

My friend's balance is given by

[tex]y=340+10t[/tex]

Average rate is given by

[tex]\dfrac{t(6)-t(2)}{6-2}\\ =\dfrac{(340+10\times 6)-(340+10\times 2)}{4}\\ =\mathbf{10}[/tex]

My balance grows faster than my friends balance.