dr. jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left…

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. there were bacteria after 5 hours.

Answer

Explanation:

Step1: Identify the decay - formula

This is an exponential decay problem. The formula for exponential decay is $N = N_0\times r^t$, where $N_0$ is the initial amount, $r$ is the decay factor, and $t$ is the time. Here, $N_0 = 100$, $r=0.9$ (since 90% or 0.9 of the bacteria remain each hour), and $t = 5$.

Step2: Substitute the values into the formula

$N=100\times(0.9)^5$.

Step3: Calculate $(0.9)^5$

$(0.9)^5=0.9\times0.9\times0.9\times0.9\times0.9 = 0.59049$.

Step4: Calculate $N$

$N = 100\times0.59049=59.049$.

Step5: Round to the nearest whole number

Rounding 59.049 to the nearest whole number gives 59.