A town has a population of 2000 and grows at 4% every year write an equation to represent the scenario
1 answer:
Answer: .
Step-by-step explanation:
It is given that,
Initial population of a town = 2000
Growth rate = 4% = 0.04 per year
The exponential growth function for population is
where, is initial population, r is growth rate and t is number of years.
Substitute in the above equation.
Therefore, the required equation is , where P is population after t years.
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Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let and
. Then, the given equation is essentially
. Thus, we can use the chain rule.
Recall the chain rule: . So, let's find the derivative of each function:
We can use the Power Rule here:
Now:
Again, use the Power Rule and Sum Rule
Now, we can put them together: