The population of a country decreases by 1% each decade. What was the population in 2000 if in  2030 the population is 1940598.

To solve this problem, we need to determine the population in the year 2000, given that the population decreases by 1% each decade and the population in 2030 is 1,940,598.

### Step 1: Understand the Decay Formula
The population decrease can be modeled by the formula:

\[
P(t) = P_0 \times (1 - r)^t
\]

Where:
- \( P(t) \) is the population at time \( t \) years after the initial time.
- \( P_0 \) is the initial population (in this case, in the year 2000).
- \( r \) is the decay rate per decade (1% or 0.01).
- \( t \) is the number of decades between the initial time and the final time.

### Step 2: Calculate the Number of Decades Between 2000 and 2030
From 2000 to 2030, the time span is 30 years, which is equivalent to 3 decades.

### Step 3: Apply the Population Formula
We can use the given population in 2030 and solve for \( P_0 \):

\[
1,940,598 = P_0 \times (1 - 0.01)^3
\]

Simplifying further:

\[
1,940,598 = P_0 \times (0.99)^3
\]

Calculate \( (0.99)^3 \):

\[
(0.99)^3 = 0.970299
\]

So,

\[
1,940,598 = P_0 \times 0.970299
\]

### Step 4: Solve for \( P_0 \)
Now, divide both sides by 0.970299 to find \( P_0 \):

\[
P_0 = \frac{1,940,598}{0.970299} \approx 2,000,000
\]

So, the population in the year 2000 was approximately **2,000,000**.

Would you like more details or have any questions? Here are some related questions to consider:

1. How would the formula change if the population decreased by 2% each decade?
2. What would the population be in 2040, continuing the same 1% decrease per decade?
3. How would you calculate the population in 1990, given the 1% decrease per decade?
4. Can this decay model be applied to a situation where the decrease is not constant but varies by decade?
5. How would you model the population if the decrease is compounded continuously instead of every decade?

**Tip:** Understanding exponential decay and growth can help you model a variety of real-world situations, from population dynamics to financial investments.

Explore how to calculate the population in the year 2000 given a 1% decrease per decade and knowing the population in 2030 is 1,940,598. Understand exponential decay in real-world scenarios.

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