Question

If a new antibiotic is added to the culture, the number of bacteria is reduced by half every hour, then the function that models the number of bacteria remaining in the culture after the antibiotic is added, is

• A. A linear function
• B. A quadratic function
• C. A polynomial function
• D. An exponential function

Answer 1

The correct option is D An exponential function

The given problem states that the bacteria is reduced by half every hour.
Let us assume the bacteria level is $2000$, then after half an hour the bacteria is reduced to $2000\times \frac{1}{2}=1000$ and next another half an hour the bacteria is reduced $t$ $1000\frac{1}{2}=500$ and so on. The change in the number of bacteria is a common ratio $\frac{1}{2}$.

So, the best model is an exponential function of the form $y=a{\left(\frac{1}{2}\right)}^x$, where $a=$ bacteria level.