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.

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• Anonymous
10 years ago

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)

≈ 1460000.

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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.

• 10 years ago

Source(s): 199
• 10 years ago

1462037.581

For how

52000=25000(1+r/100)^9

from thise find r and insert in the below formula § find x.

x=25000(1+r/100)^50

x