Math Problem Statement
A certain type of bacteria increases at a steady rate of 20% per hour, if there were 100 bacteria at t = 0, how many bacteria would there after seven hours??
Solution
The growth of bacteria follows the formula for exponential growth:
Where:
- is the population after time ,
- is the initial population,
- is the growth rate (as a decimal),
- is the time in hours.
In this case:
- ,
- (20% growth rate per hour),
- hours.
Now, plugging the values into the formula:
Let's calculate that.
I'll compute the value.After 7 hours, the bacteria population will have grown to approximately 358.
Would you like further details or have any questions?
Here are 5 related questions to expand on this topic:
- How would the population change if the growth rate were 30% instead of 20%?
- What would be the population after 10 hours at the same growth rate?
- How can you calculate the time it takes for the population to double?
- What happens if the growth rate decreases over time?
- How would you model bacteria growth if the rate changes each hour?
Tip: In exponential growth, small changes in the growth rate can lead to significant differences over time!
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Math Problem Analysis
Mathematical Concepts
Exponential Growth
Algebra
Formulas
N(t) = N_0 × (1 + r)^t
Theorems
-
Suitable Grade Level
Grades 9-12
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