A ball is dropped from a height of 3 m. After each bounce it rises to 75% of its previous height.
a) State t1 and r: t1 = 3 m r = 0.75
b) Write the general term for the sequence:
tn = (t1)(r^n-1)
tn = (3)(0.75^n-1)
c) What height does the ball reach after the 6th bounce? (I am not sure how to do this question)
This was my attempt: I suppose you solve for tn and you plug in 6 into n...
tn = (3)(0.75^6-1)
tn = (3)(0.75^5)
tn = (3)(.2373046875)
tn = .7119140625
My answer was wrong, the answer is 53.39 cm.
d) After how many bounces will the ball reach a height of approx. 40 cm? (I cannot solve this one either)
My attempt: I plugged in 40 cm into tn and try to solve for n:
40 = (3)(0.75^n-1)
13.3 = 0.75^n-1 I am stuck here... I do not know how to get n alone with algebra....
The answer is 7 times.
Could anyone tell me where I went wrong for c) and d) and what I should have done? Thanks!