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

i think its a and d

step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!