a biologist is monitoring the hourly growth of bacteria when introduced to an anti - bacterial. the…

a biologist is monitoring the hourly growth of bacteria when introduced to an anti - bacterial. the functions $f(t)=500(2^{t})$ and $g(t)=750(2^{t})$ 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.\nis the biologists sum correct? use the drop - down menus to explain.\n$f(t)+g(t)=1250(4^{t})$\nclick the arrows to choose an answer from each menu.\nto 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...\nthe biologists sum choose... correct.

a biologist is monitoring the hourly growth of bacteria when introduced to an anti - bacterial. the functions $f(t)=500(2^{t})$ and $g(t)=750(2^{t})$ 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.\nis the biologists sum correct? use the drop - down menus to explain.\n$f(t)+g(t)=1250(4^{t})$\nclick the arrows to choose an answer from each menu.\nto 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...\nthe biologists sum choose... correct.

Answer

Explanation:

Step1: Recall rule for adding exponential terms

When adding exponential terms with the same base, we add the coefficients. Here, the base of both $f(t)=500(2^{t})$ and $g(t)=750(2^{t})$ is $2^{t}$.

Step2: Calculate the sum

$f(t)+g(t)=(500 + 750)(2^{t})=1250(2^{t})$. The biologist incorrectly multiplied the exponents when adding the functions. The correct sum is $1250(2^{t})$ not $1250(4^{t})$.

Answer:

To add the functions, the biologist should: add the coefficients of the exponential expressions. The sum of the functions is $f(t)+g(t)=1250(2^{t})$. The biologist's sum is not correct.