A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation?
A) y = 1,000(1.15)6; 2,313 bacteria
B) y = 1,000(1.15)7; 2,660 bacteria
C) y = 1,000(1.5)5; 7,594 bacteria
D) y = 1,000(1.5)6; 11,391 bacteria
Answers
Given : A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day.
To Find : What is the population of the culture 6 days after inoculation
y = 1,000(1.15)⁶; 2,313 bacteria
y = 1,000(1.15)⁷; 2,660 bacteria
y = 1,000(1.5)⁵; 7,594 bacteria
y = 1,000(1.5)⁶; 11,391 bacteria
Solution:
On start of 1 st day = 1000
After 1 Day = 1000(1 + 15/100) = 1000(1.15)
After 2 Day3 = 1000(1.15)(1.15) = 100(1.15)²
After 3 Days = 100(1.15)³
After 4 Days = 100(1.15)⁴
After 5 Days = 100(1.15)⁵
After 6 Days = 100(1.15)⁶ = 2,313
population of the culture 6 days after inoculation = 100(1.15)⁶ = 2,313
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Question:
A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation?
Answer:
On first day = 1000
- After 1 day = 1000(1.15)
- After 2 day = 1000(1.15)²
- After 3 day = 1000(1.15)³
- After 4 day = 1000(1.15)^4
- After 5 day = 1000(1.15)^5
- After 6 day = 1000(1.15)^6 = 2313.
The population of culture 6 days after inoculation = 1000(1.15)^6 = 2313.