Answer:
The area after 13 years will be 1141 km2
Step-by-step explanation:
This problem can be modeled with an exponencial equation:
A = Ao * (1+r)^t
Where A is the Area after t years, Ao is the inicial area and r is the rate that the area changes.
For our problem, we have that Ao = 2300, r = -5,25% = -0.0525 and t = 13.
Then, we can find the area after 13 years:
A = 2300 * (1 - 0.0525)^13
A = 2300 * (0.9475)^13 = 1140.93 km2
Rounding to the nearest square kilometer, we have A = 1141 km2
The answer is choice A, a 3.5% increase.
12/15 = 80%
13/17 = 76.47%
80% - 76.47% = 3.5%
Answer:

General Formulas and Concepts:
<u>Algebra I</u>
- Exponential Rule [Rewrite]:

<u>Calculus</u>
Limits
- Right-Side Limit:

Limit Rule [Variable Direct Substitution]: 
Derivatives
Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Integrals
Integration Constant C
Integration Rule [Fundamental Theorem of Calculus 1]: 
Integration Property [Multiplied Constant]: 
U-Substitution
U-Solve
Improper Integrals
Exponential Integral Function: 
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Integrate Pt. 1</u>
- [Integral] Rewrite [Exponential Rule - Rewrite]:

- [Integral] Rewrite [Improper Integral]:

<u>Step 3: Integrate Pt. 2</u>
<em>Identify variables for u-substitution.</em>
- Set:

- Differentiate [Basic Power Rule]:

- [Derivative] Rewrite:

<em>Rewrite u-substitution to format u-solve.</em>
- Rewrite <em>du</em>:

<u>Step 4: Integrate Pt. 3</u>
- [Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Integral] Substitute in variables:

- [Integral] Rewrite [Integration Property - Multiplied Constant]:

- [Integral] Substitute [Exponential Integral Function]:
![\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(u)] \bigg| \limits^1_a](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E1_0%20%7B%5Cfrac%7B1%7D%7Bxe%5E%7Bx%5E2%7D%7D%20%5C%2C%20dx%20%3D%20%5Clim_%7Ba%20%5Cto%200%5E%2B%7D%20%5Cfrac%7B1%7D%7B2%7D%5BEi%28u%29%5D%20%5Cbigg%7C%20%5Climits%5E1_a)
- Back-Substitute:
![\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-x^2)] \bigg| \limits^1_a](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E1_0%20%7B%5Cfrac%7B1%7D%7Bxe%5E%7Bx%5E2%7D%7D%20%5C%2C%20dx%20%3D%20%5Clim_%7Ba%20%5Cto%200%5E%2B%7D%20%5Cfrac%7B1%7D%7B2%7D%5BEi%28-x%5E2%29%5D%20%5Cbigg%7C%20%5Climits%5E1_a)
- Evaluate [Integration Rule - FTC 1]:
![\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-1) - Ei(a)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%5Climits%5E1_0%20%7B%5Cfrac%7B1%7D%7Bxe%5E%7Bx%5E2%7D%7D%20%5C%2C%20dx%20%3D%20%5Clim_%7Ba%20%5Cto%200%5E%2B%7D%20%5Cfrac%7B1%7D%7B2%7D%5BEi%28-1%29%20-%20Ei%28a%29%5D)
- Simplify:

- Evaluate limit [Limit Rule - Variable Direct Substitution]:

∴
diverges.
Topic: Multivariable Calculus