A bacteria population increases every hour. At 12pm there are 5 cells. At 1pm there are 10 cells. At 2pm there are 20 cells. At 3pm there are 40 cells. If this pattern continues, how many cells will there be at 7pm? The bacteria cells double each hour in the example above. From 3pm to 7pm, we have 4 hours, meaning 4 doubling periods. Which is 2 * 2 * 2 * 2 or 2^4. So we have: 40 * 2^4 40 * 16 = [B]640 cells[/B]

A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be in 10 years? Find the number of doubling periods: Number of Doubling periods = Time / Doubling period Number of Doubling periods = 10/2 Number of Doubling periods = 5 Create a function to determine the amount of bunnies after each doubling period: B(n) = 45 * 2^n Since we calculated 5 doubling periods, we want B(5): B(5) = 45 * 2^5 B(5) = 45 * 32 B(5) = [B]1,440[/B]

A certain culture of the bacterium Streptococcus A initially has 8 bacteria and is observed to double every 1.5 hours.After how many hours will the bacteria count reach 10,000. Set up the doubling times: 0 | 8 1.5 | 16 3 | 32 4.5 | 64 6 | 128 7.5 | 256 9 | 512 10.5 | 1024 12 | 2048 13.5 | 4096 15 | 8192 16.5 | 16384 So at time [B]16.5[/B], we cross 10,000 bacteria.

A city doubles its size every 48 years. If the population is currently 400,000, what will the population be in 144 years? Calculate the doubling time periods: Doubling Time Periods = Total Time / Doubling Time Doubling Time Periods = 144/48 Doubling Time Periods = 3 Calculate the city population where t is the doubling time periods: City Population = Initital Population * 2^t Plugging in our numbers, we get: City Population = 400,000 * 2^3 City Population = 400,000 * 8 City Population = [B]3,200,000[/B]

A colony of 995 bacteria doubles in size every 206 minutes. What will the population be 618 minutes from now? Calculate the doubling time periods: Doubling Time Periods = Total Minutes From Now / Doubling Period in Minutes Doubling Time Periods = 618/206 Doubling Time Periods = 3 Calculate the new population using the doubling time formula below where t is the number of doubling periods: Population = Initial Population * 2^2 Population = 995 * 2^3 Population = 995 * 8 Population = [B]7,960[/B]

A culture of bacteria doubles every hour. If there are 500 bacteria at the beginning, how many bacteria will there be after 9 hours? Assumptions and givens; [LIST] [*]h is the number of hours. [*]B(h) is the number of bacteria at time h [*]B(0) is the starting bacteria amount [*]Doubling means multiplying by 2, so we have: [/LIST] B(h) = B(0) * 2^h We want h = 9, so we have: B(9) = 500 * 2^9 B(9) = 500 * 512 B(9) = [B]256,000[/B]

A population of wolves on an island starts at 5 if the population doubles every 10 years, what will be the population in 90 years? If the population doubles every 10 years, we have 90/10 = 9 doubling periods. Our population function P(t) is where t is the doubling period P(t) = 5(2^t) The problem asks for P(9): P(9) = 5(2^9) P(9) = 5(512) P(9) = [B]2,560[/B]

A towns population is currently 500. If the population doubles every 30 years, what will the population be 120 years from now? Find the number of doubling times: 120 years / 30 years per doubling = 4 doubling times Set up our growth function P(n) where n is the number of doubling times: P(n) = 500 * 2^n Since we have 4 doubling times, we want P(4): P(4) = 500 * 2^4 P(4) = 500 * 16 P(4) = [B]8,000[/B]

In a hurricane the wind pressure varies directly as the square of the wind velocity. If a wind pressure is a measure of a hurricane's destruction capacity, what happens to this destructive power when the wind speed doubles? Let P = pressure and v = velocity (wind speed) We are given p = v^2 Double velocity, so we have a new pressure P2: P2 = (2v)^2 P2 = 4v^2 Compare the 2: p = v^2 p = 4v^2 Doubling the wind speed [B]quadruples, or 4 times[/B] the pressure.

Mike received a penny on December 1st. On December 2nd he received 2 cents. December 3rd another 4 cents and December 4th he received 8 cents. If his money continues to double, how much will he earn on December 25th? We have 24 doubling times starting December 2 to December 25 0.01 * 2^24 0.01 * 16,777,216 [B]167,772.16[/B]

Free Population Doubling Time Calculator - Determines population growth based on a doubling time.

Free Rule of 72 Calculator - Calculates how long it would take money to double (doubling time) using the rule of 72 interest approximation as well as showing the mathematical proof of the Rule of 72.

The doubling time of a population of flies is 8 hours. a) By what factor does a population increase in 24 hours? b) By what factor does the population increase in 2 weeks? a) If the population doubles every 8 hours, then it doubles 3 times in 24 hours, since 24/8 = 3. So 2 * 3 = 6. The increase factor is [B]6[/B] b) Since a) is one full day, we now need to know how much it doubles in 14 days, which is 2 weeks. We take our factor of 6 for each day, and multiply it by 14: 14 * 6 = [B]84[/B]

The population of a town doubles every 12 years. If the population in 1945 was 11,005 people, what was the population in 1981? Calculate the difference in years: Difference = 1981 - 1945 Difference = 36 Calculate doubling periods: Doubling periods = Total years / Doubling time Doubling periods = 36/12 Doubling periods = 3 Population = Initial Population * 2^doubling periods Population = 11005 * 2^3 Population = 11005 * 8 Population = [B]88,040[/B]

the sum of doubling a number and 100 which totals to 160 Take this algebraic expression in pieces: [LIST=1] [*]Let the number be n. [*]Double it, means we multiply n by 2: 2n [*]The sum of this and 100 means we add 100 to 2n: 2n + 100 [*]The phrase [I]which totals[/I] means we set 2n + 100 equal to 160 [/LIST] [B]2n + 100 = 160[/B] <-- This is our algebraic expression If the question asks you to solve for n, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B100%3D160&pl=Solve']type this equation into our search engine[/URL] and we get: [B]n = 30[/B]

Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies? Let d = every 2 days. We set up the exponential equation 2 * 2^d = 600,000 Divide each side by 2: 2^d = 300000 To solve this equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=2%5Ed%3D300000&pl=Calculate']type it in our math engine[/URL] and we get d = 18.19 (2 day periods) 18.19 * days per period = 36.38 total days Most problems like this ask you to round to full days, so we round up to [B]37 days[/B].