Question

Suppose that the per capita growth rate of a population is $2 \% ;$ that is, if $N(t)$ denotes the population size at time $t$, then $$\frac{1}{N} \frac{d N}{d t}=0.02$$ Suppose also that the population size at time $t=2$ is equal to $100 .$ Use a linear approximation to compute the population size at time $t=2.1$.

          Suppose that the per capita growth rate of a population is $2 \% ;$ that is, if $N(t)$ denotes the population size at time $t$, then
$$\frac{1}{N} \frac{d N}{d t}=0.02$$
Suppose also that the population size at time $t=2$ is equal to $100 .$ Use a linear approximation to compute the population size at time $t=2.1$.

Added by Monica B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/22/2023

Step 1

02N$$ Now, we want to find the linear approximation of $N(t)$ at $t=2$. To do this, we need to find the derivative of $N(t)$ with respect to $t$ and evaluate it at $t=2$. Using the given equation, we have: $$\frac{dN}{dt} = 0.02N$$ At $t=2$, we know that $N(2) Show more…

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Suppose that the per capita growth rate of a population is $2 \% ;$ that is, if $N(t)$ denotes the population size at time $t$, then $$\frac{1}{N} \frac{d N}{d t}=0.02$$ Suppose also that the population size at time $t=2$ is equal to $100 .$ Use a linear approximation to compute the population size at time $t=2.1$.