the population of a certain geographic region is approximately 105 million and grows continuously at a relative growth rate of 1.53%. what will the population be in 5 years?
solve for A, the amount
A = 105(e^(.0153(5))
To find the population in 5 years, we can use the formula for continuous exponential growth:
P(t) = Pā * e^(rt)
Where:
P(t) = population at time t
Pā = initial population
e = base of the natural logarithm (approximately 2.71828)
r = relative growth rate (as a decimal)
t = time period in years
Given that the initial population, Pā, is 105 million and the relative growth rate, r, is 1.53% (or 0.0153 as a decimal), we can calculate the population after 5 years.
P(5) = 105,000,000 * e^(0.0153 * 5)
Step 1: Calculate the exponent
Exponent = 0.0153 * 5
Exponent = 0.0765
Step 2: Calculate e raised to the power of the exponent
e^(0.0765) = approximately 1.0791
Step 3: Multiply the result by the initial population
Population in 5 years = 105,000,000 * 1.0791
Population in 5 years ā 113,453,500
Therefore, the population of the geographic region will be approximately 113,453,500 in 5 years.