One of the tables below shows linear data and the other shows exponential data.
ID: 3012401 • Letter: O
Question
One of the tables below shows linear data and the other shows exponential data. (In this problem, round the ratio to 2 decimal places)
a)
i. Is the data for f linear? Explain Why or Why not. ii. If it is linear, give a formula for f.
iii. Is the data for f exponential?
Explain why or why not iv. If it is Exponential, give a formula for f.
b)
i. Is the data for g linear? Explain why or why not
ii. If it is linear, give a formula for g.
iii. Is the data for g exponential? Explain why or why not?
iv. If it is exponential, give a formula for g.
t 0 3 6 9 12 15 f(t) 8.5 10.53 12.56 14.59 16.62 18.65Explanation / Answer
a>
lets take a look at the slope (m) , this will give us some idea whether the data is linear or not.
slope = m = (y2-y1)/(x2-x1)
m = (10.53-8.5)/(3-0) = 2.03/3
m = (12.56-10.53)/(6-3) = 2.03/3
m = (14.59-12.56)/(9-6) = 2.03/3
m = (16.62-14.59)/(12-9) = 2.03/3
m = (18.65-16.62)/(15-12) = 2.03/3
as the slope is the same so the data is lineat in nature .
ii> the formula could be found using the point slope form as we have a point (0,8.5) or we culd take any other point as well and the slope m = 2.03/3
=> (f-f1) = m(t-t1)
f - 8.5 = (2.03/3)*(t-0)
f(t) = 2.03t/3 + 8.5 , ----------------> formula for f
iii> the function f(t) is not exponential as the growth of f(t) is linear in nature , that is with every 2.03 units of rise there is a run of 3 units towards the positive direction .
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