Question about Texas Instruments TI-30XA Calculator

# The initial population of a town is 2800, and it grows with a doubling time of 10 years. Whay wi the population be in 12 years

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The population doubles in ten years so the annual growth is the tenth root of two. The growth in twelve years is the annual growth rate raised to the twelfth power.

The tenth root of two is about 1.0718 . That value raised to the twelfth power is about 2.2974 . Multiplied by the initial population of 2800 gives 6433.

On the TI-30XA press 2 2nd [xth-root] 1 0 = y^x 1 2 * 2 8 0 0 =

Posted on Nov 05, 2012

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## Related Questions:

### How has geography changed since 1900?

Since 1900, America and Americans have experienced tremendous changes in both the makeup of the population and in how people live their lives, according to the U.S. Census Bureau.
In 1900, most people living in the United States were male, under 23 years old, lived in the country and rented their homes. Almost half of all the people in the U.S. lived in households with five or more other people.
Today, most people in the U.S. are female, 35 years old or older, live in metropolitan areas and own their own home. Most people in the U.S. now either live alone or in households with no more than one or two other people.
These are just the top-level changes reported by the Census Bureau in their 2000 report titled Demographic Trends in the 20th Century. Released during the bureau's 100th anniversary year, the report tracks trends in population, housing and household data for the nation, regions and states.
"Our goal was to produce a publication that appeals to people interested in the demographic changes that shaped our nation in the 20th century and to those interested in the numbers underlying those trends," said Frank Hobbs, who co-authored the report with Nicole Stoops. "We hope it will serve as a valuable reference work for years to come."

Some highlights of the report include:

### Population Size and Geographic Distribution

• The U.S. population grew by more than 205 million people during the century, more than tripling from 76 million in 1900 to 281 million in 2000.
• As the population grew, the geographical population center shifted 324 miles west and 101 miles south, from Bartholomew County, Indiana, in 1900 to its current location in Phelps County, Missouri.
• In every decade of the century, the population of the Western states grew faster than the populations of the other three regions.
• Florida's population rank rose more than that of any other state, catapulting it from 33rd to 4th place in state rankings. Iowa's population ranking dropped the furthest, from 10th in the nation in 1900 to 30th in 2000.

### Age

• Children under 5 years old represented the largest five-year age group in 1900 and again in 1950; but in 2000 the largest groups were 35 to 39 and 40 to 44.
• The percentage of the U.S. population age 65 and over increased in every censusfrom 1900 (4.1 percent) to 1990 (12.6 percent), then declined for the first time in Census 2000 to 12.4 percent.
• From 1900 to 1960, the South had the highest proportion of children under 15 and the lowest proportion of people 65 and over, making it the country's "youngest" region. The West grabbed that title in the latter part of the century.

### Race and Hispanic Origin

• At the beginning of the century, only 1-in-8 U.S. residents were of a race other than white; by the end of the century, the ratio was 1-in-4.
• The black population remained concentrated in the South, and the Asian and Pacific Islander population in the West through the century, but these regional concentrations declined sharply by 2000.
• From 1980 to 2000, the Hispanic-origin population, which may be of any race, more than doubled.
• The total minority population people of Hispanic origin or of races other than white increased by 88 percent between 1980 and 2000 while the non-Hispanic white population grew by only 7.9 percent.

### Housing and Household Size

• In 1950, for the first time, more than half of all occupied housing units were owned instead of rented. The homeownership rate increased until 1980, decreased slightly in the 1980s and then rose again to its highest level of the century in 2000 reaching 66 percent.
• The 1930s was the only decade when the proportion of owner-occupied housing units declined in every region. The largest increase in homeownership rates for each region then occurred in the next decade when the economy recovered from the Depression and experienced post-World War II prosperity.
• Between 1950 and 2000, married-couple households declined from more than three-fourths of all households to just over one-half.
• The proportional share of one-person households increased more than households of any other size. In 1950, one-person households represented 1-in-10 households; by 2000, they comprised 1-in-4.
For more reference see https://www.thoughtco.com/census-bureau-reports-100-years-in-america-4051546

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Let g = ln(24/20)/15 .
Then the population = 20,000,000 e^(gt) .

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### The initial population of a town 2800, and it grows with doubling time of 10 years. What wil the population be in 12 years

The population doubles in ten years so the annual growth is the tenth root of two. The growth in twelve years is the annual growth rate raised to the twelfth power.

The tenth root of two is about 1.0718 . That value raised to the twelfth power is about 2.2974 . Multiplied by the initial population of 2800 gives 6433.

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### The initial population of a town is 2800, and it grows with a doubling time of 10 years. What will the population be in 12 years

The population doubles in ten years so the annual growth is the tenth root of two. The growth in twelve years is the annual growth rate raised to the twelfth power.

The tenth root of two is about 1.0718 . That value raised to the twelfth power is about 2.2974 . Multiplied by the initial population of 2800 gives 6433.

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### A(24)=40,000e((ln2/26)24)

your best bet in any kind of exponential equation is to set up the general form of the equation and then solve for the constants with the numbers they gave you. With P being population, t being time, you know it is going to look like P=Ae^(b*t) and you are given 2 P's for 2 t's.

So for the first set :

Eq 1 P(26)=40,000=Ae^(b*26)

and the second being a time t=0 P was half the current value:

Eq 2 P(0)=20,000=Ae^(b*0)
20,000=A*1 so A=20,000

now b from Eq 1

40,000=20,000e^(b*26)

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