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2 years ago

After how many months will colony 2 always have more bacteria than colony 1?

Mathematics

1 answer:

MaRussiya [10]2 years ago

6 0

The true statement is that colony 2 will always have more bacteria than colony 1 after 4 months

<h3>How to determine the number of months?</h3>

The functions are given as:

Colony 1: f(x) = x^2
Colony 2: g(x) = 2^x

When colony 2 has more bacteria than colony 1, then it means that:

g(x) >f(x)

Substitute the function values

2^x > x^2

From the graph of both functions, we have:

2^x > x^2 at x >4

This means that colony 2 will always have more bacteria than colony 1 after 4 months

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Let's solve!

Step-by-step explanation:

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$then$

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If the equation looks like this, then it has the solution

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Another answer is

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Critical value for 95% confidence interval = $z_{\alpha/2}=1.96$

Confidence interval :

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.76\pm(1.96)\sqrt{\dfrac{0.76(1-0.76)}{1000}}\\\\=0.76\pm0.0264708866493\\\\\approx0.76\pm0.0265\\\\=(0.76-0.0265,\ 0.76+0.0265)=(0.7335,\ 0.7865)$

Hence, the 95% confidence interval for the true percent of registered voters in Flagstaff who support immigration reform: $(0.7335,\ 0.7865)$

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