Question

1. in a children’s story, double dan the dragonfly is growing fast. his body length is doubling every month. at the beginning of the story, his length is 1 cm. a) create a table to show how dan’s body length increases every month for ten months. b) what is his body length five months after the beginning of the story? express your answer as a power. then, evaluate. c) after how many months is his body length more than 50 cm?

Explanation:

Step1: Create the table for part a)

Month	Length (cm)
1	\(2=2^{1}\)
2	\(4 = 2^{2}\)
3	\(8=2^{3}\)
4	\(16 = 2^{4}\)
5	\(32=2^{5}\)
6	\(64 = 2^{6}\)
7	\(128=2^{7}\)
8	\(256 = 2^{8}\)
9	\(512=2^{9}\)
10	\(1024 = 2^{10}\)

Step2: Solve part b)

The formula for the length \(L\) after \(n\) months is \(L = 2^{n}\). For \(n = 5\), the length as a power is \(2^{5}\).
Evaluate \(2^{5}=2\times2\times2\times2\times2=32\)

Step3: Solve part c)

We check the powers of 2:
\(2^{5}=32\), \(2^{6}=64\)

Answer:

a) The table is shown above.
b) As a power: \(2^{5}\), evaluated: \(32\) cm.
c) After \(6\) months.