Question
A biologist is monitoring the hourly growth of bacteria when introduced to an anti-bacterial. The
functions f (t) = 500 (2*) and g (t) = 750 (2*) model the growth rate of the same type of
bacteria in two Petri dishes for t hours. The biologist adds the functions to determine the total number of bacteria during the first stage of the experiment. His sum is given below.
Is the biologist's sum correct? Use the drop-down menus to explain.
f (t) + (t) = 1250 (4*)
Click the arrows to choose an answer from each menu.
To add the functions, the biologist should Choose…..
add the
coefficients of the exponential expressions. The sum of the functions is f (t) + g(t) = Choose...
The biologist's sum
Choose...
correct.
functions f (t) = 500 (2*) and g (t) = 750 (2*) model the growth rate of the same type of
bacteria in two Petri dishes for t hours. The biologist adds the functions to determine the total number of bacteria during the first stage of the experiment. His sum is given below.
Is the biologist's sum correct? Use the drop-down menus to explain.
f (t) + (t) = 1250 (4*)
Click the arrows to choose an answer from each menu.
To add the functions, the biologist should Choose…..
add the
coefficients of the exponential expressions. The sum of the functions is f (t) + g(t) = Choose...
The biologist's sum
Choose...
correct.
Answers
GPT-4o mini
To determine if the biologist's sum is correct, we need to analyze the functions and how they are added.
1. The biologist has two functions:
- \( f(t) = 500 \cdot 2^t \)
- \( g(t) = 750 \cdot 2^t \)
2. When adding these two functions, we combine the coefficients of the exponential:
\[
f(t) + g(t) = 500 \cdot 2^t + 750 \cdot 2^t = (500 + 750) \cdot 2^t = 1250 \cdot 2^t
\]
3. Therefore, the biologist's combined function should be:
\[
f(t) + g(t) = 1250 \cdot 2^t
\]
Based on this analysis:
- **To add the functions, the biologist should**: **add the coefficients of the exponential expressions.**
- **The sum of the functions is \( f(t) + g(t) = 1250 \cdot 2^t \).**
- **The biologist's sum**: **is correct.**
So, the final answer would be:
- **To add the functions, the biologist should**: **add the coefficients of the exponential expressions.**
- **The sum of the functions is \( f(t) + g(t) = 1250 \cdot 2^t \).**
- **The biologist's sum**: **is correct.**
1. The biologist has two functions:
- \( f(t) = 500 \cdot 2^t \)
- \( g(t) = 750 \cdot 2^t \)
2. When adding these two functions, we combine the coefficients of the exponential:
\[
f(t) + g(t) = 500 \cdot 2^t + 750 \cdot 2^t = (500 + 750) \cdot 2^t = 1250 \cdot 2^t
\]
3. Therefore, the biologist's combined function should be:
\[
f(t) + g(t) = 1250 \cdot 2^t
\]
Based on this analysis:
- **To add the functions, the biologist should**: **add the coefficients of the exponential expressions.**
- **The sum of the functions is \( f(t) + g(t) = 1250 \cdot 2^t \).**
- **The biologist's sum**: **is correct.**
So, the final answer would be:
- **To add the functions, the biologist should**: **add the coefficients of the exponential expressions.**
- **The sum of the functions is \( f(t) + g(t) = 1250 \cdot 2^t \).**
- **The biologist's sum**: **is correct.**