Question

Write an exponential function to model the situation. Find each amount after the specified time.. . A population of 1,860,000 decreases 1.5% each year for 12 years.

Answer 1

To model the situation, use the exponential decay formula P(t) = P₀ * (1 - r)^t, where P(t) is the population after time t, P₀ is the initial population, and r is the decay rate. Substitute the given values into the formula to find the exponential function and then find the population after 12 years by substituting t = 12 into the function.

Step-by-step explanation:

To model the situation, we can use the exponential decay formula:

P(t) = P₀ * (1 - r)t

Where P(t) is the population after time t, P₀ is the initial population, and r is the decay rate. In this case, P₀ = 1,860,000 and r = 0.015 (1.5% as a decimal). So the exponential function to model the situation is:

P(t) = 1,860,000 * (1 - 0.015)t

To find the population after 12 years, we can substitute t = 12 into the function:

P(12) = 1,860,000 * (1 - 0.015)12

Answer 2

Answer: The amount after the specified time is 155148.54.

Step-by-step explanation:

Since We have given that

Initial Population = 186000

Rate of decrement = 1.5%

Time period = 12 years

Since we need to use "Exponential function ":

`Amount=P(1-r)^t\\\\Amount=186000(1-(1.5)/(100))^(12)\\\\Amount=186000(1-0.015)^(12)\\\\Amount=186000(0.985)^(12)\\\\Amount=155148.54`

Hence, the amount after the specified time is 155148.54.