Chapter 10: Q. 10.33 (page 1017)

Another researcher at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts his experiment with $50$ of the bacteria that grows at a rate of $15 %$ per hour. He will check on the bacteria every $8$ hours. How many bacteria will he find in $8$ hours?

Short Answer

Expert verified

The researcher will find $166.0058$ bacteria in $8$ hours, if there are $50$ at the beginning and growing at a rate of $15 %$ per hour.

Step by step solution

Step 1. Given

There are $50$ bacteria growing at a rate of $15 %$ per hour.

To find the number of bacteria at the end of $8$ hour.

Step 2. Formula for exponential growth or decay

For an original amount, $A_{0}$ , that grows or decays at a rate, $r$ , for a certain time, $t$ , the final amount, $A$ , is:

$A = A_{0} e^{r t}$

Step 3. Identify the values of each variable in the formula.

From the given,

$A_{0} = 50 r = 0.15 / h o u r t = 8$

Step 4. Substitute the values in the formula

Substitute the values in the formula:

$A = A_{0} e^{r t} = 50 e^{0.15 (8)} = 166.0058$

The bacteria after $8$ hours is $166.0058$

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Another researcher at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts his experiment with $50$ of the bacteria that grows at a rate of $15 %$ per hour. He will check on the bacteria every $8$ hours. How many bacteria will he find in $8$ hours?

Short Answer

Step by step solution

Step 1. Given

Step 2. Formula for exponential growth or decay

Step 3. Identify the values of each variable in the formula.

Step 4. Substitute the values in the formula

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Another researcher at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts his experiment with 50of the bacteria that grows at a rate of 15%per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours?

Short Answer

Step by step solution

Step 1. Given

Step 2. Formula for exponential growth or decay

Step 3. Identify the values of each variable in the formula.

Step 4. Substitute the values in the formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Statistics

Calculus

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Another researcher at the Center for Disease Control and Prevention, Lisa, is studying the growth of a bacteria. She starts his experiment with $50$ of the bacteria that grows at a rate of $15 %$ per hour. He will check on the bacteria every $8$ hours. How many bacteria will he find in $8$ hours?