Mr. Science has a pair of hamsters. The hamsters have 2 babies. Those babies grow up and have 2 babies of their own.
Write the number of baby hamsters from the previous day as a numeral expression using exponential notation. How many babies are there all together.
To write the number of baby hamsters from the previous day as a numeral expression using exponential notation, we first need to determine the growth pattern.
We are given that Mr. Science has a pair of hamsters, which means there are initially 2 hamsters. These hamsters have 2 babies, and then these babies grow up and have 2 babies of their own.
Let's break down the growth pattern:
- Initially: 2 hamsters
- First generation: 2 babies
- Second generation: 2 babies of each of the first generation hamsters
To represent this growth pattern using exponential notation, we can use the fact that each generation doubles the previous generation. Since there are 3 generations in total, we can express it as:
2^3
This means that the number of baby hamsters from the previous day can be written as 2 raised to the power of 3, which simplifies to:
2^3 = 8 baby hamsters
To find the total number of babies all together, we need to add the number of babies from each generation. In this case, we have:
2 babies from the first generation
2 babies × 2 from the second generation (as each hamster from the first generation has 2 babies)
8 babies from the third generation (as calculated earlier)
Adding these numbers together gives us:
2 + 2 × 2 + 8 = 2 + 4 + 8 = 14 babies
So, there are a total of 14 baby hamsters all together.