Connect with knowledgeable individuals and find the best answers at IDNLearn.com. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.
Sagot :
To determine the number of bacteria present at different times for this certain product, we'll be using the function [tex]\( f(t) = 500e^{0.1t} \)[/tex], where [tex]\( t \)[/tex] is the time in days. Let's find the number of bacteria at [tex]\( t = 2 \)[/tex] days, [tex]\( t = 3 \)[/tex] days, and [tex]\( t = 7 \)[/tex] days (which is equivalent to 1 week).
Let's go through each time point step-by-step:
### (a) 2 days
1. Plug [tex]\( t = 2 \)[/tex] into the function [tex]\( f(t) = 500e^{0.1t} \)[/tex].
2. Compute the expression [tex]\( 500e^{0.1 \times 2} \)[/tex].
After computation:
- The result is approximately 611 million bacteria.
- Rounding to the nearest integer, we have 611 million bacteria at 2 days.
### (b) 3 days
1. Plug [tex]\( t = 3 \)[/tex] into the function [tex]\( f(t) = 500e^{0.1t} \)[/tex].
2. Compute the expression [tex]\( 500e^{0.1 \times 3} \)[/tex].
After computation:
- The result is approximately 675 million bacteria.
- Rounding to the nearest integer, we have 675 million bacteria at 3 days.
### (c) 1 week (7 days)
1. Plug [tex]\( t = 7 \)[/tex] into the function [tex]\( f(t) = 500e^{0.1t} \)[/tex].
2. Compute the expression [tex]\( 500e^{0.1 \times 7} \)[/tex].
After computation:
- The result is approximately 1007 million bacteria.
- Rounding to the nearest integer, we have 1007 million bacteria at 7 days.
### Summary:
- At 2 days, the approximate number of bacteria is 611 million.
- At 3 days, the approximate number of bacteria is 675 million.
- At 1 week (7 days), the approximate number of bacteria is 1007 million.
These approximations are rounded to the nearest integer as required.
Let's go through each time point step-by-step:
### (a) 2 days
1. Plug [tex]\( t = 2 \)[/tex] into the function [tex]\( f(t) = 500e^{0.1t} \)[/tex].
2. Compute the expression [tex]\( 500e^{0.1 \times 2} \)[/tex].
After computation:
- The result is approximately 611 million bacteria.
- Rounding to the nearest integer, we have 611 million bacteria at 2 days.
### (b) 3 days
1. Plug [tex]\( t = 3 \)[/tex] into the function [tex]\( f(t) = 500e^{0.1t} \)[/tex].
2. Compute the expression [tex]\( 500e^{0.1 \times 3} \)[/tex].
After computation:
- The result is approximately 675 million bacteria.
- Rounding to the nearest integer, we have 675 million bacteria at 3 days.
### (c) 1 week (7 days)
1. Plug [tex]\( t = 7 \)[/tex] into the function [tex]\( f(t) = 500e^{0.1t} \)[/tex].
2. Compute the expression [tex]\( 500e^{0.1 \times 7} \)[/tex].
After computation:
- The result is approximately 1007 million bacteria.
- Rounding to the nearest integer, we have 1007 million bacteria at 7 days.
### Summary:
- At 2 days, the approximate number of bacteria is 611 million.
- At 3 days, the approximate number of bacteria is 675 million.
- At 1 week (7 days), the approximate number of bacteria is 1007 million.
These approximations are rounded to the nearest integer as required.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.