Suppose that the population (in millions) of Paraguay in 2007 was 6.7 and that the expected continuous annual rate of change of the population is $0.024$. Find the exponential growth model $P = C e ^ { k t }$ for the population by letting $t = 0$ correspond to 2000 . Round your answer to four decimal places.
A) $P = 6.7000 e ^ { 0.024 t }$
B) $P = 5.6639 e ^ { 0.024 t }$
C) $P = 5.3984 e ^ { 0.024 t }$
D) $P = 5.8014 e ^ { 0.024 t }$
E) $P = 5.5296 e ^ { 0.024 t }$

Question

Quizplus · Accepted Answer

First, we rewrite the growth rate in decimal form: $0.024 = 0.024 \cdot 1 = 0.024 \cdot {\frac{1}{100}}$. This means that the annual rate of change is 2.4%. From 2000 to 2007 is a span of 7 years, so let t = 7. Then we have:
$$6.7 = C e ^ { 0.024 \cdot 7 }$$
$$6.7 = C e ^ { 0.168 }$$
$$C = \frac{6.7}{e ^ { 0.168 }} \approx 5.6639$$
Therefore, the exponential growth model is:
$$P = 5.6639 e ^ { 0.024 t }$$

Suppose That the Population (In Millions) of Paraguay in 2007 0.0240.0240.024

Suppose That the Population (In Millions) of Paraguay in 2007 $0.024$