sat-dog

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^xh, in meters, of her best pole vault for that year. The = x relationship can be written as h^xh Ca , where C and a are positive constants. = =1.23 1.23 It’s given that when x 0, h^xh . Substituting 0 for x and for h^xh in = x 1.23= 0 1.23= 1.23 = x h^xh Ca yields Ca , or C. Substituting for C in h^xh Ca =1.23 x = =1.54 yields h^xh a . It’s also given that when x 2, h^xh . Substituting 2 for 1.54 =1.23 x 1.54=1.23 2 x and for h^xh in h^xh a yields a . Dividing each side of this equation by 1.23 yields 1 1 . . 2 5 3 4 = 1 1 .2 .2 3 3a 2 , or a 2 is approximately equal to 1.252 . 1.252 1.12 1.12 Since a is positive, a is approximately equal to , or . Substituting =1.23 x =1.23 1.12 x for a in h^xh a yields h^xh ^ h . = Choice A is incorrect. When x 0, the value of h^xh in this function is equal to 1.12 1.23 rather than , and it is decreasing rather than increasing. Choice B is = 1.12 incorrect. When x 0, the value of h^xh in this function is equal to rather 1.23 than . Choice C is incorrect. This function is decreasing rather than increasing.