Answer:

To find the population of the town in 1986 we can use the exponential growth formula:

P(t) = P0 * (1 + r)^t

Where:

P(t) is the population at time t

P0 is the initial population (in 1986)

r is the growth rate (in this case r=2 since the population doubles every decade)

t is the number of years

Let's use this formula to solve the problem:

Given:

P0 (population in 1986) = ?

P(t) (population in 2016) = 52000

r (growth rate) = 2

t (number of years) = 2016 - 1986 = 30

Plugging in the values:

52000 = P0 * (1 + 2)^30

Now we need to solve for P0 (population in 1986):

(1 + 2)^30 = 52000 / P0

3^30 = 52000 / P0

Taking the 30th root of both sides:

3 = (52000 / P0)^(1/30)

Taking the reciprocal:

1/3 = (P0 / 52000)^(1/30)

Now let's solve for P0 by raising both sides to the power of 30:

1/3^30 = P0 / 52000

P0 = (1/3^30) * 52000

Calculating the result:

P0 = 52000 / (3^30)

Using a calculator we find that P0 ≈ 18.25

Therefore the population in the town in 1986 was approximately 18250.

Verified answer

Answer:

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Sure, I can help you with that. The exponential solution is as follows:

```

Let P be the population of the town in 1986.

Then P * 2^10 = 52000, where 10 is the number of decades between 1986 and 2016.

Solving for P, we get P = 52000 / 2^10 = 6500.

```

Therefore, the population of the town in 1986 was **6500**.

Here is a step-by-step explanation of the solution:

1. The population of the town doubles every decade. This means that the population is multiplied by 2 each time a decade passes.

2. In 2016, the population of the town was 52,000.

3. We want to find the population of the town in 1986, which is 30 years before 2016.

4. 30 years is 3 decades.

5. So, the population of the town in 1986 is 52,000 / 2^3 = 6500.

I hope this helps! Let me know if you have any other questions.