a barangay has 1000 individuals and its population doubles every 60 years. Give an exponential model for the barangay's populati

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Svet_ta [12.7K] · Answer 1 · 2026-03-26T12:02:21+03:00

Answer:

P(t) = 1000e^(0.01155)t

Step-by-step explanation:

The population of the barangay can be modeled using the exponential function;

P(t) = P0e^kt

P(t) reflects the population after t years

P0 denotes the initial population

t indicates the time

With an initial population of 1000, we set P0 = 1000

Given that the population doubles every 60 years, at t = 60, it holds that P(t) = 2P0

Inserting that into the equation yields

2P0 = P0e^k(60)

2 = e^60k

Taking the natural logarithm of both sides

ln2 = lne^60k

ln2 = 60k

k = ln2/60

k = 0.01155

Inserting the determined k value and P0 into the function gives

P(t) = 1000e^(0.01155)t

Thus, the exponential model for the population of the barangay is

P(t) = 1000e^(0.01155)t