Question

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.

Explanation:

Step1: Add the functions

We know that \(f(t)=500(2^{t})\) and \(g(t)=750(2^{t})\). When adding them, we use the distributive property \(a\times c + b\times c=(a + b)\times c\). Here \(a = 500\), \(b=750\) and \(c = 2^{t}\). So \(f(t)+g(t)=(500 + 750)\times2^{t}\).

Step2: Calculate the sum of coefficients

\(500+750 = 1250\), so \(f(t)+g(t)=1250\times2^{t}\).

Step3: Analyze the biologist's sum

The biologist's sum is \(f(t)+g(t)=1250(4^{t})\). Since \(4^{t}=(2\times2)^{t}=2^{t}\times2^{t}
eq2^{t}\), the biologist's sum is incorrect.

Answer:

No, the biologist's sum is incorrect. The correct sum is \(f(t)+g(t)=1250(2^{t})\) not \(1250(4^{t})\).