the population of a city is expected to triple every 25 years . when can the city planners expect the present population of 180 persons to double?

since every 25 years the population grows by a factor of 3,

P(y) = 180*3^(y/25)

2(180) = 180*3(y/25)
2 = 3^(y/25)
ln2 = y/25 ln3
y = 25*ln2/ln3
= 15.77

A population of 500 triples every year. What will the population be after 3 years?

To find out when the present population of 180 persons will double, we need to determine the growth rate based on the given information that the population is expected to triple every 25 years.

Let's go through the process step by step:

1. Start by calculating the growth factor: The city's population is expected to triple every 25 years. So, the growth factor is 3 (tripling the population) per 25 years.

2. Determine the number of growth periods required for the population to double: Since we want to find out when the current population of 180 persons will double, we need to determine the number of times the population needs to triple to reach a value twice as large.

To do this, we can use the formula:

Number of periods = log2(Target Population / Current Population) / log2(Growth Factor)

Target Population = 2 * Current Population = 2 * 180 = 360

Using the growth factor of 3 and the current population of 180, we can calculate:

Number of periods = log2(360 / 180) / log2(3)

3. Calculate the result: Use a calculator or math software to evaluate the above expression and find the value of "Number of periods." This will determine how many multiples of 25 years are needed for the population to double.

Now, let's calculate the result: