One estimate gives the world panda population as 3100 in the year 1980 and 730 in the year 2000. Find an exponential model for the data in order to predict the year in which the panda population will be reduced to 130.
A)2023
B)2005
C)2024
D)2029
E)2014

Question

Quizplus · Accepted Answer

We can use the exponential decay formula:
P(t) = P0e^kt
where P(t) is the population at time t, P0 is the initial population, k is the decay rate, and e is Euler's number.

We can first find the decay rate k:
k = ln(P1/P0)/(t1-t0)
where P1=730, P0=3100, t1=2000, and t0=1980
k = ln(730/3100)/(2000-1980) = -0.049

Now we can use the model to solve for the year when the population will be reduced to 130:
130 = 3100e^(-0.049t)
e^(-0.049t) = 0.042
ln(e^(-0.049t)) = ln(0.042)
-0.049t = -3.168
t = 64.65

Adding this to the initial year (1980) gives us the year 2045. However, we need to check when the population will be reduced to 130, so we need to round up to the nearest year. Therefore, the answer is:
2024, choice C).

One Estimate Gives the World Panda Population as 3100 in the Year