Question

A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 • 3^x models the number of bacteria after x hours.

Graph the function. (You do not need to submit the graph).

Use the graph to estimate when there will be about 550 bacteria in the culture.

Answer 1

Well, you will have a graph that resembles natural growth, although it is not natural growth. So something like this..

For your second problem, you want to know when will there be about 550 bacteria. What you can do is solve for y=550.\[550=350*3^x\]Divide by 350,\[\frac{11}{7}=3^x\]Take the logarithm of base 3 if you use a calculator, on both sides and you get,\[x=\log_{3}{\frac{11}{7}} \approx 0.41\]So approximately after 0.41 hours you will have 550 bacteria.

Answer 2

estimate means estimate, but you can solve directly if you know logarithms

\[550=35\times 3^x\]
\[\frac{110}{7}=3^x\]
\[x=\frac{\ln(\frac{110}{7})}{\ln(3)}\] then a calculator

Answer 3

I am sorry, I mistook 35 with 350. Just make the following correction,\[\frac{110}{7}=3^x\]and now,\[x=\log_{3}{\frac{110}{7}} \approx 2.507\]

Answer 4

as for finding log base 3, your calculator probably will not have it, which is why you need the change o' base formula
\[A=b^x\iff x=\frac{\ln(A)}{\ln(b)}\]