An investment account was opened with an infttal value of GBBO. The value of the account doubled every 10 years Which equation represents the value of the account M(t) án dollars, t years after the account was opened? M(t)=800((1)/(2))^(t)/(10) D M(t)=800((1)/(10))^t M(t)=800(2)^(t)/(10) D M(t)=800(10)^t

To determine the correct equation representing the value of the investment account, we need to consider that the account's value doubles every 10 years. This is a classic example of exponential growth.<br /><br />The general formula for exponential growth is:<br /><br />\[ M(t) = M_0 \times (r)^{\frac{t}{T}} \]<br /><br />where:<br />- \( M(t) \) is the amount of money at time \( t \),<br />- \( M_0 \) is the initial amount of money,<br />- \( r \) is the growth factor,<br />- \( T \) is the time period over which the growth factor applies.<br /><br />In this case:<br />- The initial value \( M_0 \) is given as 800.<br />- The account doubles every 10 years, so the growth factor \( r \) is 2.<br />- The time period \( T \) is 10 years.<br /><br />Plugging these values into the formula gives:<br /><br />\[ M(t) = 800 \times (2)^{\frac{t}{10}} \]<br /><br />Therefore, the correct equation is:<br /><br />\[ M(t) = 800(2)^{\frac{t}{10}} \] <br /><br />This matches option C in your list.