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Math  /  Calculus

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DETAILS MY NOTES TANAPMATH7 3.3.005. PRACTICE ANOTHER population (in billions) as a function of time tt (in years), with t=0t=0 corresponding to the beginning of 1990. (Round your answers to two decimal places.) (a) If the world population continues to grow at approximately 2%/year2 \% / y e a r, find the length of time t4t_{4} (in yr) required for the population to quadruple in size. t4=t_{4}= □\square yr (b) Using the time t4t_{4} found in part (a), what would be the world population (in billions of people) if the growth rate were reduced to 1.7%/yr1.7 \% / y r ? □\square billion people Need Help? Read it Watch it

Studdy Solution
Using the time t4≈69.32 t_4 \approx 69.32 years, calculate the population if the growth rate is reduced to 1.7% 1.7\% :
P(t4)=P0⋅e0.017×69.32 P(t_4) = P_0 \cdot e^{0.017 \times 69.32}
Calculate the exponent:
0.017×69.32≈1.17844 0.017 \times 69.32 \approx 1.17844
Calculate P(t4) P(t_4) :
P(t4)=P0⋅e1.17844 P(t_4) = P_0 \cdot e^{1.17844}
P(t4)≈P0⋅3.25 P(t_4) \approx P_0 \cdot 3.25
The population would be approximately 3.25 3.25 times the initial population, in billions.
The time required for the population to quadruple is:
69.32 years \boxed{69.32} \text{ years}
The population with a reduced growth rate would be approximately:
3.25 billion people \boxed{3.25} \text{ billion people}

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