In the year 2000 there were 350 mobile phones users living in the small town of Phoneville. Since 2000 the number of residents using mobile phones has increased by 25% each year, that is, each year the number of mobile phones increases by a factor of 1.25

Question

In the year 2000 there were 350 mobile phones users living in the small town of Phoneville. Since 2000 the number of residents using mobile phones has increased by 25% each year, that is, each year the number of mobile phones increases by a factor of 1.25

Calculate, to three significant figures, the number of mobile phone users after 19 years. You may find it useful to first devise a formula for the number of mobile phone users after n years.

Answer 1

number of mobile phones

= 350(1.25)^19 = 24 286.13

I thought Phoneville was a small town?

Answer 2

Thanks! I've no idea, i thought my answr was too far off but I was using the wrong formula. Thanks!

Answer 3

Oh, dear Phoneville, where everyone is always connected! Let's calculate the number of mobile phone users after 19 years using my handy formula.

Starting with 350 mobile phone users in the year 2000, the number of mobile phones increases by a factor of 1.25 each year. In mathematics language, we can call this "compounding growth."

To calculate the number of mobile phone users after n years, we can use the formula:

Number of mobile phone users = 350 * (1.25)^n

Plugging in n = 19, we have:

Number of mobile phone users = 350 * (1.25)^19

Now, let's compute that value and bring on the laughter!

Number of mobile phone users after 19 years = 350 * (1.25)^19 ≈ 1589.698

So, with three significant figures, the number of mobile phone users after 19 years in Phoneville is approximately 1590. Just don't be surprised if you see a bunch of clowns with mobile phones around town!

Answer 4

To calculate the number of mobile phone users after 19 years, you can use the formula for exponential growth:

F = P * (1 + r)^n

Where:
F is the final number of mobile phone users after n years.
P is the initial number of mobile phone users (350 in the year 2000).
r is the growth rate per year (25% or 0.25 expressed as a decimal).
n is the number of years (19 in this case).

Plugging in the values into the formula:

F = 350 * (1 + 0.25)^19

Calculating the expression inside the parentheses first:

F = 350 * (1.25)^19

Now you can raise 1.25 to the power of 19:

F = 350 * 5.56992040069

Finally, multiply the initial number of mobile phone users by the result:

F ≈ 1949.4721402

Rounding to three significant figures, the number of mobile phone users after 19 years is approximately 1950.