Question

1. suppose there is an apocalypse simulation study and a zombie infestation begins with one zombie, and spreads at a quick rate. the zombie population can be modeled by $z(n) = \frac{175000n + 150}{5n + 150}$, where $n$ is the number of days after the apocalypse began. how many days will it take for the zombie population to reach 24,000? round up to the nearest day.\

$\frac{175000n + 150}{5n + 150} = 24000$\
$175000n + 150 = 24000(5n + 150)$\
$17500n + 150 = $

Explanation:

Step1: Set up the equation

We know that \( Z(n)=\frac{175000n + 150}{5n+150} \) and we want to find \( n \) when \( Z(n) = 24000 \). So we set up the equation:

$$ \frac{175000n+150}{5n + 150}=24000 $$

Step2: Cross - multiply

Multiply both sides of the equation by \( 5n + 150 \) to get rid of the denominator:

$$ 175000n+150=24000\times(5n + 150) $$

Step3: Expand the right - hand side

Using the distributive property \( a(b + c)=ab+ac \), where \( a = 24000 \), \( b = 5n \) and \( c = 150 \), we have:

$$ 175000n+150=24000\times5n+24000\times150 $$

$$ 175000n+150 = 120000n+3600000 $$

Step4: Move all \( n \) terms to one side and constants to the other

Subtract \( 120000n \) from both sides and subtract 150 from both sides:

$$ 175000n-120000n=3600000 - 150 $$

$$ 55000n=3599850 $$

Step5: Solve for \( n \)

Divide both sides by 55000:

$$ n=\frac{3599850}{55000}\approx65.45 $$

Step6: Round up

Since we need to round up to the nearest day, \( n = 66 \)

Answer:

66