The mass of a sample of the chemical element einsteinium-253253253 after it is initially measured is represented by the following table: Time (weeks)Mass (grams)
000400400400
333201201201
666989898
999505050
121212242424
151515121212
Which model for M(t)M(t)M, left parenthesis, t, right parenthesis, the mass of the sample ttt weeks after it's initially measured, best fits the data?

-23.99048X + 310.7619

Step-by-step explanation:

Given the following :

Time(weeks) - - - mass(grams)

0 - - - - - - - - - - - - - 400

3 - - - - - - - - - - - - - 201

6 - - - - - - - - - - - - - 98

9 - - - - - - - - - - - - - 50

12 - - - - - - - - - - - - 24

15 - - - - - - - - - - - - 12

Using the regression calculator, the model for Mass(time), which best fits the data is represented by the equation:

ŷ = -23.99048X + 310.7619

Where, - 23.99044 is the slope or gradient

X is the time(t)

y is the Mass

310.7619 is the intercept. Point where the graph crosses the y-axis.

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.