Question

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.

Answer 1

If the intial count was 100,000 bacteria, after one hour 90% decrease => 10 % stands => 100,000*0.1 bacetria. After two hours 90% decrease => 10% stands => 100,000*0.1^2. After three hours, they stand 100,000 * 0.1^3. After four hours, 100,000*0.1^4 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).

Answer 2

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:

$y = 59$