x h x 0 1.23 2 1.54 4 1.94 The table shows the exponential relationship between the number of years,

Question

x h x 0 1.23 2 1.54 4 1.94 The table shows the exponential relationship between the number of years, x , since Hana started training in pole vault, and the estimated height h x , in meters, of her best pole vault for that year. Which of the following functions best represents this relationship, where x d 4 ?

Accepted Answer

Choice D is correct. The table shows an increasing exponential relationship between the number of years, x , since Hana started training in pole vault and the estimated height h x , in meters, of her best pole vault for that year. The relationship can be written as h x = C a x , where C and a are positive constants. It's given that when x = 0 , h x = 1.23 . Substituting 0 for x and 1.23 for h x in h x = C a x yields 1.23 = C a 0 , or 1.23 = C . Substituting 1.23 for C in h x = C a x yields h x = 1.23 a x . It's also given that when x = 2 , h x = 1.54 . Substituting 2 for x and 1.54 for h x in h x = 1.23 a x yields 1.54 = 1.23 a 2 . Dividing each side of this equation by 1.23 yields 1.54 1.23 = 1.23 a 2 1.23 , or a 2 is approximately equal to 1.252 . Since a is positive, a is approximately equal to 1.252 , or 1.12 . Substituting 1.12 for a in h x = 1.23 a x yields h x = 1.23 1.12 x . Choice A is incorrect. When x = 0 , the value of h x in this function is equal to 1.12 rather than 1.23 , and it is decreasing rather than increasing. Choice B is incorrect. When x = 0 , the value of h x in this function is equal to 1.12 rather than 1.23 . Choice C is incorrect. This function is decreasing rather than increasing.

$x$	$h (x)$
$0$	$1.23$
$2$	$1.54$
$4$	$1.94$

Question 2a0b1f