To solve this problem, we'll follow the same steps as before, using the exponential growth formula:

$P(t) = P_0 \cdot e^{rt}$

Step 1: Find the growth rate $r$

Given:

• In 1930 ($t = 0$): $P_0 = 25000$
• In 1970 ($t = 40$): $P(40) = 30000$

Using the formula:

$30000 = 25000 \cdot e^{40r}$

We can solve for $r$:

$\frac{30000}{25000} = e^{40r}$

$\ln\left(\frac{30000}{25000}\right) = 40r$

$r = \frac{1}{40} \cdot \ln\left(\frac{30000}{25000}\right)$

Step 2: Calculate the population in 2000

To find the population in 2000 ($t = 70$):

$P(70) = 25000 \cdot e^{70r}$

Let's calculate the values for $r$ and $P(70)$.The population of the city in the year 2000 is approximately 34,396.

Would you like further details or have any questions?

Here are 5 related questions that expand on this topic:

1. How would the population in 2000 change if the growth rate was calculated using a different time interval?
2. What would the population be in 1980 using the same exponential growth model?
3. How does this population growth compare to the first city's growth rate?
4. What factors could cause deviations from this predicted population in real life?
5. How can exponential growth be applied to predict other phenomena, like financial investments?

Tip: When working with exponential growth, small changes in the growth rate or time period can lead to significant differences in the results.