What is inductive reasoning? How are the given equivalences related? Do they follow a pattern?
104 ^(∘)F
Practice makes perfect
We use inductive reasoning when we use examples to find other similar cases or a general pattern. In this case, we will use the given examples to find the equivalent of 40 °C in Fahrenheit. Let's analyze the given examples to see if we can find a pattern.
Temperature in °C
Temperature in ° F
10
50
20
68
30
86
40
?
We can see that there is a clear pattern. Each time the temperature in °C rises by 10, the equivalent in °F rises by 18.
Temperature in ° C
Temperature in ° F
10
50
10 + 10 = 20
50 + 18 = 68
20 + 10 = 30
68 + 18 = 86
30 + 10 = 40
86 + 18 = 104
Therefore, the equivalent temperature for 40 °C is 104 °F.
Extra
Writing a General Rule
Furthermore, following the same rule, if we start from 10 ° C = 50 ° F and move backwards, we can see that these two expressions are equivalent.
10- 10 &= 0 ° C
50- 18 &= 32 ° F
We can use this to create a general formula. Starting from 0 ° C = 32 ° F, and considering that each time the temperature in ° C rises by 10, the equivalent in ° F rises by 18. We can write the equation.
° F = 18/10° C + 32
