A scientist counts 35 bacteria present in a culture and finds the the number of bacteria triples each hour. The function y= 35×3^x models the number of bacteria after x hours.
A. Graph the function
B. Use the graph to estimate when there will be about 550 bacteria in the culture.

Question

A scientist counts 35 bacteria present in a culture and finds the the number of bacteria triples each hour. The function y= 35×3^x models the number of bacteria after x hours. 
A. Graph the function
B. Use the graph to estimate when there will be about 550 bacteria in the culture.

aaronandyson · Answer

This one will be:

Given function 

$$y = 35 \times 3^x$$

When the count of bacteria is 550 in the culture the function will be:

$$550 = 35 \times 3^x$$

Now divide 550 by 35

$$\frac{ 550 }{ 35 } = 3^x$$

Divide the L.H.S(Or the Left-hand side). by 5.

550/5 = 110
35/5 = 7

$$\frac{ 550 }{ 35 } = 3^x$$
 
when divided by 5 gives

$$\frac{ 110 }{ 7 } = 3^x$$

aaronandyson · Answer

$$\frac{ 550 }{ 35 } = 3^x$$

equals
$$\frac{ 110 }{ 7 } = 3^x$$

equals

$$x = \ln (\frac{ 110 }{ 7 } ) /\ln (3)$$

then use a calculator.

aaronandyson · Answer

ln(110 / 7) / ln(3) = 2.50731786 

In approximately 2.51 hours.

alicia.marie018 · Answer

Thank you

aaronandyson · Answer

Where is my medal..?