Math / Calculus

QuestionSuppose that the population of wolves is initially 300 , and that the rate of change of the population is given by $\mathrm{r}(\mathrm{t})$ , where t is in years. What is the meaning of $300+\int_{0}^{3} r(t) d t$ The change in the number of wolves over 3 years The total number of wolves after 3 years. The rate of change of the number of wolves in year 3

Studdy Solution

STEP 1

1. The initial population of wolves is 300.
2. The rate of change of the population is given by the function $r(t)$ .
3. The integral $\int_{0}^{3} r(t) \, dt$ represents the accumulated change in the population over the interval from $t = 0$ to $t = 3$ .

STEP 2

1. Understand the meaning of the integral $\int_{0}^{3} r(t) \, dt$ .
2. Determine what $300 + \int_{0}^{3} r(t) \, dt$ represents.
3. Match the interpretation to one of the given options.

STEP 3

The integral $\int_{0}^{3} r(t) \, dt$ represents the total change in the wolf population over the period from $t = 0$ to $t = 3$ years.

STEP 4

The expression $300 + \int_{0}^{3} r(t) \, dt$ represents the initial population of wolves (300) plus the total change in the population over 3 years.

STEP 5

The expression $300 + \int_{0}^{3} r(t) \, dt$ is the total number of wolves after 3 years, as it accounts for the initial population and the accumulated change over the 3-year period.
The correct interpretation is: The total number of wolves after 3 years.

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