A city's population is currently 365,000. If the population doubles every 24 years, what will the population be 96 years from now?

Answer 1

96 years is 4 24-year cycles. So the population will double 4 times from a starting population of 365,000.

When something doubles, it increases by a factor of 100%. That's 1.0 as a decimal.

The equation is P = I( 1 + r)ⁿ where P is the population 96 years from now, I is the initial population of 365,000 and n is the number of cycles. P = 365,000(1 + 1)⁴ = 365,000(2)⁴ = 365,000(16) = 5,840,000.

You could also make a table:

Time Pop'n

0 365,000

24 730,000

48 1,460,000

72 2,920,000

96 5,840,000

Answer 2

We're asked if a population doubles every 24 years, what will the population be in 96 years.

To answer this we have to know how many times the population will double in 96 years. If the population doubles in 24 years we just have to figure out how many "doublings" will occur by the time we get to 96 years.

Let's go step by step:

The population will double the 1st time in 24 years

The population will double the 2nd time after 24 + 24 or 48 years

The population will double the 3rd time after 24 + 24 + 24 or 72 years

The population will double the 4th time after 24 + 24 + 24 + 24 or 96 years. Bingo! It will double 4 times in 96 years.

We could also have used division to figure this out: 24 goes into 96 4 times (or 96 / 24 = 4)

Now that we know the population will double 4 times, we can calculate the future population as:

365,000 * 2 * 2 * 2 * 2 or 365,000 * 2 ^ 4 = 5,840,000

Answer 3

P(t) = 365000(2)^96/24

Can you calculate and answer?