City leaders estimate that the current population of a city is 9.73 × 10^5 people. They predict that the population will increase by 1.3 × 10^4 people each year over the next decade. According to their prediction, which is the best estimate for the city's population in 4 years?

Question

A.
10.25 × 10^10 people
B.
1.493 × 10^11 people
C.
1.025 × 10^6 people
D.
1.493 × 10^6 people

Answer 1

To estimate the city's population in 4 years, we start with the current population and add the predicted increase over the next 4 years.

1. Current Population:
   \( 9.73 \times 10^5 \) people

2. Annual Increase:
   \( 1.3 \times 10^4 \) people per year

3. Increase Over 4 Years:
   To find the increase over 4 years, we multiply the annual increase by 4: \[ \text{Total increase} = 1.3 \times 10^4 \times 4 = 5.2 \times 10^4 \]

4. Calculating the population in 4 years:
   We can add the total increase to the current population: \[ \text{Population in 4 years} = 9.73 \times 10^5 + 5.2 \times 10^4 \]

   To add these two numbers, first express \( 5.2 \times 10^4 \) in terms of \( 10^5 \): \[ 5.2 \times 10^4 = 0.52 \times 10^5 \]

   Now we can add them: \[ 9.73 \times 10^5 + 0.52 \times 10^5 = (9.73 + 0.52) \times 10^5 = 10.25 \times 10^5 \]

5. Converting to Scientific Notation:
   We express this in standard scientific notation: \[ 10.25 \times 10^5 = 1.025 \times 10^6 \]

6. Conclusion:
   The best estimate for the city's population in 4 years is: \[ \text{Option C: } 1.025 \times 10^6 \text{ people} \]