D. Solve the following problems.
1.) Suppose that the current population of a certain country grows at annual rate of 2.5%.if the current population is 7million, what be the population after 15years? what will be the annual rate if the population each to 23 million in 10 years ?
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Step-by-step explanation:
To find the population after 15 years, we can use the formula:
P = P₀(1 + r)ᵗ
where P is the future population, P₀ is the current population, r is the annual growth rate expressed as a decimal, and t is the time in years.
Plugging in the given values, we have:
P = 7,000,000(1 + 0.025)¹⁵
P ≈ 10,482,472
Therefore, the population after 15 years will be approximately 10,482,472.
To find the annual rate if the population is to reach 23 million in 10 years, we can use the same formula and solve for r:
23,000,000 = 7,000,000(1 + r)¹⁰
Dividing both sides by 7,000,000 and taking the 10th root, we have:
1 + r = (23/7)^(1/10)
1 + r ≈ 1.084
Subtracting 1 from both sides, we get:
r ≈ 0.084
Therefore, the annual rate would need to be approximately 8.4% for the population to reach 23 million in 10 years.