Estimate population in 2010?
The population of Tempe, AZ was 25,000 in 1960. In 1969, it was around 52,000. Estimate the population in 2010, assuming the exponential model holds.
Please show work.
- Anonymous9 years agoFavorite Answer
The exponential model for population is
P(t) = P_0 * e^(kt),
where t is the amount of time passed, P is the population at time t, P_0 is the population when t = 0, e is the mathematical constant (e ≈ 2.718281828), and k is a constant.
"The population of Tempe, AZ was 25,000 in 1960."
Since we're given the population in 1960, then it makes sense to let t be the number of years that have passed since 1960. Therefore, P_0 = 25000.
"In 1969, it was around 52,000."
In other words, when t = 9, P = 52000 (the t = 9 is because 1969 is 9 years after 1960). By plugging in this information into to the equation P(t) = P_0 * e^(kt), and plugging in 25000 for P_0, we can solve for k:
52000 = 25000 * e^(k * 9)
2.08 = e^(9k)
ln (2.08) = 9k
ln (2.08) / 9 = k.
Therefore, our full equation for P(t) is
P(t) = 25000 * e^([ln (2.08) / 9] * t).
"Estimate the population in 2010, assuming the exponential model holds."
In other words, we want to compute P(50) (because 2010 is 50 years after 1960).
P(50) = 25000 * e^([ln (2.08) / 9] * 50)
NOTE: You could also solve the problem by choosing to let t measure the year (instead of the years since 1960). This would give you a different value for k, but it would give you the same final answer.
- 9 years ago
About 2000 millionSource(s): 199
- 9 years ago
from thise find r and insert in the below formula § find x.