Time (years) Total amount (dollars) 0 670.00 1 674.02 2 678.06 Sara opened a savings account at a bank. The

Question

Time (years) Total amount (dollars) 0 670.00 1 674.02 2 678.06 Sara opened a savings account at a bank. The table shows the exponential relationship between the time t , in years, since Sara opened the account and the total amount d , in dollars, in the account. If Sara made no additional deposits or withdrawals, which of the following equations best represents the relationship between t and d ?

Accepted Answer

Choice B is correct. It&rsquo;s given that the relationship between t and d is exponential. The table shows that the value of d increases as the value of t increases. Therefore, the relationship between t and d can be represented by an increasing exponential equation of the form d = a 1 + b t , where a and b are positive constants. The table shows that when t = 0 , d = 670 . Substituting 0 for t and 670 for d in the equation d = a 1 + b t yields 670 = a 1 + b 0 , which is equivalent to 670 = a 1 , or 670 = a . Substituting 670 for a in the equation d = a 1 + b t yields d = 670 1 + b t . The table also shows that when t = 1 , d = 674.02 . Substituting 1 for t and 674.02 for d in the equation d = 670 1 + b t yields 674.02 = 670 1 + b 1 , or 674.02 = 670 1 + b . Dividing both sides of this equation by 670 yields 1.006 = 1 + b . Subtracting 1 from both sides of this equation yields b = 0.006 . Substituting 0.006 for b in the equation d = 670 1 + b t yields d = 670 1 + 0.006 t . Therefore, of the choices, choice B best represents the relationship between t and d . Choice A is incorrect and may result from conceptual or calculation errors. Choice C 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)
$0$	$670.00$
$1$	$674.02$
$2$	$678.06$

Question time-y