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. is the biologists sum correct? use the drop - down menus to explain. f(t)+g(t)=1250(4^t) 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 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. is the biologists sum correct? use the drop - down menus to explain. f(t)+g(t)=1250(4^t) 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 biologists sum choose... correct.

Answer

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.

Explanation:

Step1: Identify like - terms

The functions $f(t) = 500(2^{t})$ and $g(t)=750(2^{t})$ have the same exponential part $2^{t}$.

Step2: Apply addition rule for like - terms

When adding $a\cdot b^{x}$ and $c\cdot b^{x}$, we use the rule $(a + c)\cdot b^{x}$. Here $a = 500$, $c = 750$ and $b^{x}=2^{t}$, so $f(t)+g(t)=(500 + 750)\cdot2^{t}=1250(2^{t})$.

Step3: Compare with biologist's sum

The biologist's sum is $1250(4^{t})$, which is incorrect as we should keep the base of the exponential term as $2$ when adding these functions.