Question

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.?

Answer 1

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

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

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

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