The population of Longview is 4^7

Question

. The population of Springhill is 4^10
. Milltown's population is 4^−2
of Springhill. Which city's population is greater: Longview or Milltown?

Answer 1

To compare the populations of Longview and Milltown, let's first express everything using a common base.

1. Longview Population: \[ \text{Population of Longview} = 4^7 \]

2. Springhill Population: \[ \text{Population of Springhill} = 4^{10} \]

3. Milltown Population: Milltown's population is \( 4^{-2} \) of Springhill's population, which we can calculate as: \[ \text{Population of Milltown} = 4^{-2} \times 4^{10} \] Using the property of exponents \( a^m \times a^n = a^{m+n} \): \[ \text{Population of Milltown} = 4^{-2 + 10} = 4^{8} \]

Now we need to compare the populations of Longview and Milltown:

• Longview: \( 4^7 \)
• Milltown: \( 4^8 \)

Since \( 4^8 \) (Milltown) is greater than \( 4^7 \) (Longview), we can conclude that:

\[ \text{Milltown's population is greater than Longview's population.} \]