Question

A hot air balloon is descending.
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×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 1

Answer:

The height of the balloon at 09 18 =  788.4 meters.

Step-by-step explanation:

As the hot air balloon is descending.

and the height of the balloon n minutes after it starts to descend is $h_{n}$

meters.

The height of the balloon (n +1) minutes after it starts to descend, $h_{n+1}$meters, is given by

$h_{n+1}$= $k *h_{n}+20$ where K is a constant

Here the balloon starts to descend from a height of 1200 meters at 09 15

So $h_{n}$=1200 meters

At 09 16 the height of the balloon is 1040 meters.

So  $h_{n+1}$= 1040 meters

the height of the balloon at 09 18 = $h_{n+3}$ meters

now  $h_{n+1}$= $k *h_{n}+20$

k = $\frac{h_{n+1 }-20 }{h_{n} }$

k= (1040 - 20) ÷ 1200

k = 0.85

Now $h_{n+2}$ = (0.85 × 1040) +20 =904 meters

Similarly  $h_{n+3}$ = (0.85 × 904) +20 = 788.4 meters.

Therefore the height of the balloon at 09 18 =  788.4 meters.

Learn more about decending height here- https://brainly.ph/question/14542904

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