One of the tables below shows linear data and the other show

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.

Solution

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 .