The population of guatemala in 2000 was 12.7 million.
1. assuming exponential growth, what would be the size of the population after time t (measured in years after 2000) if the population was 30 million in 2020? answer (in millions): p(t)=
2. assuming exponential growth, what would be the size of the population after time t (measured in years after 2000) if the population was 30 million in 2125?
answer (in millions): p(t)=

Since the population of Guatemala follows an exponential growth, therefore the equation describing the population over time should be in the form:

p = p0 (1 + r)^t

where,

p = is the population at specified time t

p0 = is the initial population (measured starting year 2000) = 12.7 m

r = the growth rate

t = time in years

A. Calculating for the growth rate r when p = 30 and t = 20:

30 = 12.7 (1 + r)^20

1 + r = (30 / 12.7)^(1/20)

r = (30 / 12.7)^(1/20) – 1

r = 0.0440

So the equation is:

p = p0 (1.0440)^t

B. Calculating for the growth rate r when p = 30 and t = 125:

30 = 12.7 (1 + r)^125

1 + r = (30 / 12.7)^(1/125)

r = (30 / 12.7)^(1/125) – 1

r = 0.0069

So the equation is:

p = p0 (1.0069)^t

step-by-step explanation:

try remembering the steps

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.