Pearson Algebra 1 Common Core, 2011
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Exercise 23 Page 73

What is inductive reasoning? How are the given equivalences related? Do they follow a pattern?

40°C= 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