Question

A machine in a laboratory is set to steadily increase the temperature inside. The temperature in degrees Celsius inside the machine after being turned on is a function of time, in seconds, given by the equation f(t)=22+1.3t

1. What does f(3) mean in this situation?
2. Find the value of f(3) and interpret the value.
3. What does the equation f(t)=35 mean in this situation?
4. Solve the equation to find the value of t for the question.

Answer 1

1) f(3) means the temperature after 3 seconds

2) f(3) = 22 + 1.3(3) = 25.9

Temperature after 3 seconds is 25.9°C

3) f(t) = 35 means after t seconds, temperature was 35°C

4) 35 = 22 + 1.3t

1.3t = 13

t = 10 seconds

Answer 2

Explanation:

Step 1: Answer the first question

f(3) means the temperature after 3 seconds

Step 2: Answer the second question

The value of
`f(3) = 22 + 1.3(3)` → 25.9 degrees

The value of f(3) which is 25.9 means that after 3 seconds, the temperature is 25.9 degrees.

Step 3: Answer the third question

f(t) = 35 means that after a t amount of seconds, the temperature is 35 degrees.

Step 4: Answer the fourth question

`f(t) = 35` so...
`35 = 22 + 1.3t`

`35 - 22 = 22 - 22 + 1.3t`

`13 = 1.3t`

`13 / 1.3 = 1.3t / 1.3`

`10 = t`

10 seconds