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Advanced Math / Nonlinear functions Difficulty: Easy

An investment account was opened with an initial value of $dollar sign 890$ . The value of the account doubled every $10$ years. Which equation represents the value of the account $M (t)$ , in dollars, $t$ years after the account was opened?

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Explanation

Choice C is correct. It's given that $t$ represents the number of years since the account was opened. Therefore, $StartFraction t Over 10 EndFraction$ represents the number of $10$ -year periods since the account was opened. Since the value of the account doubles during each of these $10$ -year periods, the value of the account can be found by multiplying the initial value by $StartFraction t Over 10 EndFraction$ factors of $2$ . This is equivalent to $2 Superscript StartFraction t Over 10 EndFraction$ . It's given that the initial value of the account is $dollar sign 890$ . Therefore, the value of the account $M (t)$ , in dollars, $t$ years after the account was opened can be represented by $M (t) = 890 {(2)}^{\frac{t}{10}}$ .

Choice A is incorrect. This equation represents the value of an account if the value of the account halves, not doubles, every $10$ years.

Choice B is incorrect. This equation represents the value of an account if the value of the account decreases by $90 percent sign$ , not doubles, every $2$ , not $10$ , years.

Choice D is incorrect. This equation represents the value of an account if the value of the account increases by a factor of $10$ , not doubles, every $2$ , not $10$ , years.