Time (years) Total amount (dollars) 0 604.00 1 606.42 2 608.84 Rosa opened a savings account at a bank. The

Question

Time (years) Total amount (dollars) 0 604.00 1 606.42 2 608.84 Rosa opened a savings account at a bank. The table shows the exponential relationship between the time t , in years, since Rosa opened the account and the total amount n , in dollars, in the account. If Rosa made no additional deposits or withdrawals, which of the following equations best represents the relationship between t and n ?

Accepted Answer

Choice C is correct. It&rsquo;s given that the relationship between t and n is exponential. The table shows that the value of n increases as the value of t increases. Therefore, the relationship between t and n can be represented by an increasing exponential equation of the form n = a 1 + b t , where a and b are positive constants. The table shows that when t = 0 , n = 604 . Substituting 0 for t and 604 for n in the equation n = a 1 + b t yields 604 = a 1 + b 0 , which is equivalent to 604 = a 1 , or 604 = a . Substituting 604 for a in the equation n = a 1 + b t yields n = 604 1 + b t . The table also shows that when t = 1 , n = 606.42 . Substituting 1 for t and 606.42 for n in the equation n = 604 1 + b t yields 606.42 = 604 1 + b 1 , or 606.42 = 604 1 + b . Dividing both sides of this equation by 604 yields approximately 1.004 = 1 + b . Subtracting 1 from both sides of this equation yields that the value of b is approximately 0.004 . Substituting 0.004 for b in the equation n = 604 1 + b t yields n = 604 1 + 0.004 t . Therefore, of the choices, choice C best represents the relationship between t and n . Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

Time (years)	Total amount (dollars)
$0$	$604.00$
$1$	$606.42$
$2$	$608.84$

Question time-y