Question

Kelly is recording the temperature of a cooling chemical. Using the table, determine the initial

temperature of the chemical when she poured into the beaker.

Answer 1

Initial temperature of the chemical = 97°

Explanation:

Time Temperature Difference

4 89.5 -

10 78.25 78.25 - 89.5 = -11.25

16 67.00 67 - 78.25 = -11.25

There is a common difference of -11.25 in each successive term.

Therefore, cooling of a chemical represents a linear function.

Let the function representing temperature is,

f(t) = at + b

Where 'a' = rate of change in temperature

b = initial temperature

t = time

Now 'a' =
`(y_2-y_1)/(x_2-x_1)` =
`(78.25-89.5)/(10-4)`

a = -1.875

f(t) = -1.875t + b

For t = 4 and f(t) = 89.50,

89.50 = -1.875(4) + b

b = 97

Therefore, function representing the cooling of chemical is,

f(t) = -1.875t + 97

And the initial temperature of the chemical was 97° when it was poured into the beaker.