According to the U.S. Census Bureau, the projected world population t years after 2010 is given
by the function:
f(t) = 6.947e^(0.00745t)
a. Is this equation representing a population growth or a population decay? Explain based on the
sign of the constant k = 0.00745.
b. What value of t will you use to calculate the population in 2025? Remember t is the number of
years after 2010.
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a. This equation represents population growth. This can be determined by the fact that the constant k is positive (0.00745), which means that as t increases, the value of the exponential function also increases. This indicates that the population is growing over time.
b. To calculate the population in 2025, we need to find the value of t when t = 2025 - 2010 = 15 years. So we will use t = 15 in the equation:
f(15) = 6.947e^(0.00745*15)
f(15) = 6.947e^0.11175
f(15) = 6.947 * 1.118536
f(15) ≈ 7.771 billion
Therefore, the projected world population in 2025 is approximately 7.771 billion.
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