The Population P of a Culture of Bacteria Is Described $P = 1600 e ^ { 0.052 t }$

question 35

Essay

The population P of a culture of bacteria is described by the equation $P = 1600 e ^ { 0.052 t }$ ,where t is the time,in hours,relative to the time at which the population was 1600.
(a)What was the population at $t = 3$ hours? Show your work.
(b)After how many hours will the population reach 10000.00? Round to the nearest tenth of an hour.Show your work.

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Definitions:

Macrophage

A type of white blood cell that engulfs and digests cellular debris, foreign substances, microbes, and cancer cells.

Serotonin

A neurotransmitter in the brain involved in regulating mood, appetite, and sleep, among other functions. Low levels are associated with depression.

Adrenal Gland

Endocrine glands located above the kidneys that produce various hormones, including adrenaline and steroids affecting the body's metabolism and blood pressure.

Subjective Well-Being

An individual's self-assessment of happiness and life satisfaction, considered from a personal perspective.