Julie and Brian went to the Bristol International Balloon Fiesta at the weekend.
As they watched a hot air balloon descend, they wanted to figure out how high it was.
The height of the balloon n minutes after it starts to descend is hn metres.
The height of the balloon (n+1) minutes after it starts to descend, hn+1 metres, is given by hn+1 = K x hn + 20, where K is a constant.
The balloon starts to descend from a height of 1200 metres at 09:15.
At 09:16 the height of the balloon is 1040 metres.
Work out the height of the balloon at 09:18.
Answer:
At 09:16 the balloon has descended for 1 minute. At this point we know that:
hn+1 = 1040
So:
K x 1200 + 20 = 1040
1200 K = 1020
K = 1020/1200 = 0.85
So at 9.17:
0.85 x 1040 + 20 = 904 meters
And at 9.18:
0.85 x 904 +20 = 788.40 meters