10. A coin is thrown off the top of the Statue of Liberty, which is 305 feet from the ground. The height, h, of the coin is recorded after each second, t, in
the table below. Write an equation for the curve of best fit, then predict
the height of the coin after 7 seconds.

T H
0 305
1 367
2 397
3 395
4 361

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for