Drew Williamson

2022-09-06

Bacteria X has a growth rate of 170 % per hour. Some amount of bacteria X are accidentally introduced into some fruit salad. Two hours after contamination, there were 40,000 bacteria X in the fruit salad.

Zara Pratt

Beginner2022-09-07Added 12 answers

Answer:

From the growth model of bacteria

$${N}_{t}={N}_{0}(1+\frac{r}{100}{)}^{t}\phantom{\rule{0ex}{0ex}}40000={N}_{0}(1+\frac{170}{100}{)}^{2}\phantom{\rule{0ex}{0ex}}40000={N}_{0}(2.7{)}^{2}\phantom{\rule{0ex}{0ex}}{N}_{0}=\frac{40000}{(2.7{)}^{2}}\Rightarrow {N}_{0}=5486.9686$$

Number of bacteria in the food 3 hours after contamination:

$${N}_{t}={N}_{0}(1+\frac{r}{100})\phantom{\rule{0ex}{0ex}}{N}_{t}=5486.9686(1+\frac{170}{100}{)}^{3}\phantom{\rule{0ex}{0ex}}{N}_{t}=108000$$

From the growth model of bacteria

$${N}_{t}={N}_{0}(1+\frac{r}{100}{)}^{t}\phantom{\rule{0ex}{0ex}}40000={N}_{0}(1+\frac{170}{100}{)}^{2}\phantom{\rule{0ex}{0ex}}40000={N}_{0}(2.7{)}^{2}\phantom{\rule{0ex}{0ex}}{N}_{0}=\frac{40000}{(2.7{)}^{2}}\Rightarrow {N}_{0}=5486.9686$$

Number of bacteria in the food 3 hours after contamination:

$${N}_{t}={N}_{0}(1+\frac{r}{100})\phantom{\rule{0ex}{0ex}}{N}_{t}=5486.9686(1+\frac{170}{100}{)}^{3}\phantom{\rule{0ex}{0ex}}{N}_{t}=108000$$

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