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elena55 [62]
2 years ago
7

A city has a population of 230,000 people. Suppose that each year the population grows by 8.5%. What will the population be afte

r 14
years?
Mathematics
1 answer:
worty [1.4K]2 years ago
6 0

Answer:

720,682.92

Step-by-step explanation:

8.5% = 0.085

P(t) = Initial Population * (1 + rate)t

P(t) = 230,000(1 + 0.085)t

P(t) = 230,000(1.085)t

P(14) = 230,000(1.085)14

P(14) = 720,682.82

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Given limit f(x) = 4 as x approaches 0. What is limit 1/4[f(x)]^4 as x approaches 0?
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\displaystyle 64

General Formulas and Concepts:

<u>Calculus</u>

Limits

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Limit Rule [Variable Direct Substitution Exponential]:                                         \displaystyle \lim_{x \to c} x^n = c^n

Limit Property [Multiplied Constant]:                                                                     \displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)

Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle  \lim_{x \to 0} f(x) = 4

<u>Step 2: Solve</u>

  1. Rewrite [Limit Property - Multiplied Constant]:                                           \displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4
  2. Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]:       \displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)
  3. Simplify:                                                                                                         \displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = 64

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

3 0
2 years ago
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