Sure, let's address the question step-by-step:
a. Write her age in seconds using scientific notation.
The teacher says she is just over 1 and [tex]\(\frac{1}{2}\)[/tex] billion seconds old. To express this in scientific notation, we note that 1 billion is [tex]\(1 \times 10^9\)[/tex]. So, 1 and [tex]\(\frac{1}{2}\)[/tex] billion is:
[tex]\[ 1 \times 10^9 + 0.5 \times 10^9 = 1.5 \times 10^9 \][/tex]
Thus, her age in seconds using scientific notation is:
[tex]\[ 1.5 \times 10^9 \][/tex]
b. What is a more reasonable unit of measurement for this situation?
Considering the context, a more reasonable unit of measurement for age is years, rather than seconds.
c. How old is she when you use a more reasonable unit of measurement?
To convert from seconds to years, we need to know how many seconds are in a year. There are [tex]\(60\)[/tex] seconds in a minute, [tex]\(60\)[/tex] minutes in an hour, [tex]\(24\)[/tex] hours in a day, and [tex]\(365\)[/tex] days in a year. Therefore, we have:
[tex]\[ 60 \times 60 \times 24 \times 365 = 31,536,000 \text{ seconds per year} \][/tex]
Now, convert her age in seconds to years:
[tex]\[ \text{Age in years} = \frac{1.5 \times 10^9 \text{ seconds}}{31,536,000 \text{ seconds per year}} \approx 47.564687975646876 \][/tex]
Thus, she is approximately 47.565 years old when using a more reasonable unit of measurement.
