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Dr. Jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left in the culture dish each hour. If the initial bacteria count was 100, what was the bacteria count after 5 hours? Round to the nearest whole number.

Verified Answer :

Vuk15

If the intial count was 100,000 bacteria, after one hour 90% decrease => 10 % stands => 100,0000.1 bacetria. After two hours 90% decrease => 10% stands => 100,0000.1^2. After three hours, they stand 100,000 0.1^3. After four hours, 100,0000.1^4 and after five hours 100,000*0.1^5 = 1 bacteria. Answer: 1 bacteria. If the inital count is different you just have to muliply the inicial count time (0.1^n) to get the number of bacteria after n hours, and if the number of hours is 5, then the factor is (0.1^5).

carlosego

For this case we have a function of the form:

\(y = A * (b) ^ x
\)

Where,

A: initial amount of bacteria:

b: decrease rate

x: time in hours

Substituting values we have:

\(y = 100 * (0.90) ^ x
\)

After 5 hours we have:

\(y = 100 * (0.90) ^ 5

y = 59.049
\)

Rounding to the nearest whole number:


\(y = 59
\)

Answer:

the bacterium count after 5 hours was:

\(y = 59\)

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