The towns of Franklin and Chester post their populations on signs just outside of their towns. The signs are updated once a year at the beginning of the year.
During year 111, Franklin's sign read "\text{Franklin: Population of } 20{,}000Franklin: Population of 20,000start text, F, r, a, n, k, l, i, n, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, end text, 20, comma, 000", while Chester's sign read "\text{Chester: Population of } 25{,}000Chester: Population of 25,000start text, C, h, e, s, t, e, r, colon, space, P, o, p, u, l, a, t, i, o, n, space, o, f, space, end text, 25, comma, 000". Each year, the populations grew. Specifically, Franklin's population grew by 5\%5%5, percent each year, and Chester's population grew by 500500500 people each year.
What is the first year in which Franklin's sign shows a larger number than Chester's sign?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. what a mess of redundant and uselessuselessuseless t-e-x-t !!
    after x years,
    Franklin is at 20000*1.05^x
    Chester is at 25000+500x
    so you need to solve
    20000*1.05^x > 25000+500x
    you will need to do this graphically, or using some numeric technique.
    If your calculator can solve such an equation (or you use one of the many handy online calculators), you will find that
    x ≈ 7.4

    See the graphs at*1.05%5Ex+%3E+25000%2B500x+for+-20+%3C+x+%3C+20

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. American Government

    Please check my answers 1. Which of the following make up the structure of nearly all county governments? (I need to choose 4 answers) A. Appointed bureaucrats B. Boards or commissions C. A county judge D. Elected officials E. A

  2. Trigonometry

    A passenger in an airplane flying at an altitude of 10 kilometers sees two towns directly to the left of the plane. The angles of depression to the towns are 28° and 55°. How far apart are the towns?

  3. Math

    Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand service to two nearby towns, Springfield and Shelbyville. There needs to be cable connecting Centerville to both towns. Centerville is

  4. Maths

    The scale on a map is 1 :500000, Two towns ate 7cm apart, whats the actual distance between towns. Give your answers in Km.

  1. Math, Trigonometry

    Cate is sailing her boat off the coast, which runs straight north and south. Her GPS confirms that she is 8 km from Haytown and 10 km from Beeville, two towns on the coast. The towns are separated by an angle of 80°, as seen from

  2. Utah history

    19th Century Villages and towns in Utah were often laid out according to who's plans

  3. math

    a passenger in an airplane at an altitude of a = 20 kilometers sees two towns directly to the east of the plane. The angle of depression to the towns are 55˚ and 28˚. How far apart are the towns?

  4. Geometry

    The scale on a map indicates that one inch equals 4 miles. If two towns are 3.5 inches apart on the map, what is the actual distance between the towns? 1 inch=4 miles. 3.5=x 1/4=3.5/x x=14

  1. Trigonometry

    The populations, P, of six towns with time t in years are given by: I) P=1000(1.08)^t II) P= 600(1.12)^t III) P = 2500(0.9)^t IV) P=1200(1.185)^t V) P=800(0.78)^t VI) P=2000(0.99)^t a. Which towns are growing in size? Which are

  2. math

    the scale of a mao is 1:6000000 a) the distance between 2 towns on the map is 8.7cm. what is the actual distance? 1 cm on the map repersents cm of the actual distance the actual distance between the two towns is x cm= cm= km b)

  3. English Comp

    Which of the following is an example of a primary source? A. A biography of Benjamin Franklin B. A journal article that reviews various reports on Benjamin Franklin C. A website that tells stories about Benjamin Franklin D.

  4. Math

    1) Find the angle of depression from the top of a lighthouse 250 feet above water level to the water line of a ship 2 miles off shore. arc tan 10560/250 = 88.64 ft Is this correct? 2) A passenger is in an airplane flying at n

View more similar questions or ask a new question.