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Harman [31]
3 years ago
14

Wes works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate,

and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,000 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 250,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?
Mathematics
1 answer:
Dmitry [639]3 years ago
6 0

Answer:

Correct answer: at 2 p.m. the population was 10,000

                          at 3 p.m. the population was 50,000

Step-by-step explanation:

At 1 p.m. population was 2,000

At 2 p.m. or after  first hour, the population of bacteria increases

in this way 2,000 · k  

At 3 p.m. or after second hour, the population of bacteria increases

2,000 · k²

At 4 p.m. or after third hour, the population of bacteria increases 2,000 · k³

2,000 · k³ = 250,000 =>  k³ = 250,000 / 2,000 = 125

k = ∛125 = 5  => k = 5

At 2 p.m. or after  first hour, the population of bacteria was 2,000 · 5 = 10,000

At 3 p.m. or after second hour, the population of bacteria was 2,000 · 5² =

= 2,000 · 25 = 50,000

God is with you!!!

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James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements ar
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Answer:

The expressions 7x + 4 and 3x + 5 + 4x = 1 are equivalent for every value of x.

Step-by-step explanation:

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1. When x = 2, both expressions have a value of 18. Let's find out:

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2nd expression : 3(2) + 5 + 4(2) = 1

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2.The expressions are only equivalent for x = 4 and x = 6.

This is incorrect statement as we just calculated above that the expressions are equivalent for x = 2. Hence, it is incorrect.

3. The expressions have equivalent values for any value of x.

Say, x = 0, then,

7x + 4 = 7 (0) + 4 = 4 and,

3x + 5 + 4x - 1 =  3(0) + 5 + 4(0) - 1  = 5-1 = 4

The statement holds.

Let's try again for x = 12,

7x + 4 = 7(12) + 4 = 88 and,

3x + 5 + 4x - 1 =  3(12) + 5 + 4(12) - 1  = 36 + 5 + 48 -1 =  88

Let's try again for x = 13,

7x + 4 = 7(13) + 4 = 95 and,

3x + 5 + 4x - 1 =  3(13) + 5 + 4(13) - 1  = 39 + 5 + 52 -1 =  95

Clearly, it holds for every value of x, whether it is odd or even. Hence, it is correct statement.

_______________________________________________________

Trick: 7x + 4 = 0....(1) and,

3x + 5 + 4x = 1

Rearranging the terms of above expression, we get,

(3x + 4x) + (5 - 1) =0

or 7x + 4 = 0...(2)

clearly both (1) & (2) are equivalent.

_____________________________________________________

4 0
2 years ago
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