Question

The projected population of a certain ethnic​ group(in millions) can be approximated by ​p(t)equals=39.07 left parenthesis 1.021 right parenthesis Superscript t39.07(1.021)t where tequals=0 corresponds to 2000 and 0 less than or equals t less than or equals 500≤t≤50. a. Estimate the population of this group for the year 2010. b. What is the instantaneous rate of change of the population when tequals=​10?

Answer 1

• a) p(10) ≈ 48.10
• b) about 1.00 million/year

Explanation:

a) Use t=10 in the given formula and do the arithmetic.

39.07×1.021^10 ≈ 48.0951 ≈ 48.10 . . . millions

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b) The derivative of p(t) is ...

p'(t) = p(t)·ln(1.021) ≈ 0.8120·1.021^t

p'(10) ≈ 0.99954 ≈ 1.00 . . . . millions per year