Atown has 5000 people in year t = 0. calculate how long it takes for the population p to double once, twice, and three times, assuming that the town grows at a constant rate of (a) 500 people per year. double once t = 10 correct: your answer is correct. years double twice t = 30 correct: your answer is correct. years double three times t = 70 correct: your answer is correct. years (b) 5% per year. (round your answer to three decimal places.) double once t = 14.207 correct: your answer is correct. years double twice t = 28.413 correct: your answer is correct. years double three times t = 42.620 correct: your answer is correct. years

Step-by-step explanation:

At the time t = 0, population of the town = 5000

Rate of population increase = 500 per year

Therefore, the equation that will represent the population will be

Where = Population after t years

= Initial population

t = Time in years

a). For double once the population will be 500×2 = 10000

By plugging in the values in the equation,

10000 = 5000 + 500t

500t = 10000 - 5000

500t = 5000

t =

t = 10 years

For Double twice,

Population will be = 10000×2 = 20000

Now we plug in the values in the equation again

20000 = 5000 + 500t

500t = 20000 - 5000

500t = 15000

t =

t = 30 years

For double thrice,

Population of the town = 20000×2 = 40000

Now we plug in the values in the equation,

40000 = 5000 + 500t

500t = 40000 - 5000

500t = 35000

t =

t = 70 years

b). If the population growth is 5%.

Then the growth will be exponential represented by

= Population after t years

= Initial population

t = time in years

For double once,

Population after t years = 10000

Take log on both the sides

tlog(1.05) = log2

t =

t = 14.20 years

For double twice,

Population after t years = 20000

Take log on both the sides

tlog(1.05) = log4

t =

t = 28.413 years

For double thrice

Population after t years = 40000

Take log on both the sides

tlog(1.05) = log8

t =

t = 42.620 years

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

3

step-by-step explanation: