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Scilla [17]
3 years ago
10

ASAP due really soon

Mathematics
1 answer:
Kamila [148]3 years ago
3 0

A bacteria culture starts with 500 bacteria and doubles in size every half hour.1

(a) How many bacteria are there after 3 hours?

We are told “. . . doubles in size every half hour.” Let’s make a table of the time and population:

t 0 0.5 1.0 1.5 2.0 2.5 3.0

bacteria 500 1000 2000 4000 8000 16000 32000

Thus, after three hours, the population of bacteria is 32,000.

(b) How many bacteria are there after t hours?

In t hours, there are 2t doubling periods. (For example, after 4 hours, the population has doubled 8

times.) The initial value is 500, so the population P at time t is given by

P(t) = 500 · 2

2t

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Someone please help me
allsm [11]

Answer:

Solutions: x = \frac{-3}{ 4} + i \sqrt{39},  x = \frac{-3}{4} - i \sqrt{39}

Step-by-step explanation:

Given the quadratic equation, 2x² + 3x + 6 = 0, where a =2, b = 3, and c = 6:

Use the <u>quadratic equation</u> and substitute the values for a, b, and c to solve for the solutions:

x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}

x = \frac{-3 +/- \sqrt{3^{2} - 4(2)(6)} }{2(2)}

x = \frac{-3 +/- \sqrt{9- 48} }{4}

x = \frac{-3 +/- \sqrt{-39} }{4}

x = \frac{-3 + i \sqrt{39} }{4}, x = \frac{-3 - i \sqrt{39} }{4}

Therefore, the solutions to the given quadratic equation are:

x = -\frac{3}{ 4} + i \sqrt{39} ,   x = -\frac{3}{4} - i \sqrt{39}

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