The size of a decreasing population is given by p(t)=P0(2)^-t/7 where p(t) represents the population as time, t, in years and p0 is the initial population what percent of the original population will be there after 10 years??

To find out what percentage of the original population will be there after 10 years, we need to substitute the value of time t = 10 years into the given equation for population size.

The equation given is:

p(t) = P0 * (2)^(-t/7)

where p(t) represents the population at time t in years and P0 is the initial population.

Let's substitute t = 10 into the equation:

p(10) = P0 * (2)^(-10/7)

Now we need to simplify this equation to find the population after 10 years.

Using the rules of exponents, we can rewrite (2)^(-10/7) as (1/2)^(10/7) which is equal to [(1/2)^10]^(1/7).

Calculating this exponent, we get:

[(1/2)^10] = 1/1024

Now let's substitute this value back into the equation:

p(10) = P0 * (1/1024)^(1/7)

Simplifying further:

p(10) = P0 * (1/1024)^(1/7)

To find the percentage of the original population after 10 years, we need to find the expression (p(10) / P0) * 100.

Calculating this expression, we have:

[(P0 * (1/1024)^(1/7)) / P0] * 100

The P0 cancels out:

[(1/1024)^(1/7)] * 100

Now we can evaluate this expression:

[(1/1024)^(1/7)] * 100 ≈ 5.68%

Therefore, approximately 5.68% of the original population will remain after 10 years.

To find out what percentage of the original population will be there after 10 years, we need to find the value of p(10) as a percentage of P0.

Given:
p(t) = P0(2)^(-t/7)

To find p(10), we substitute t = 10 into the equation:
p(10) = P0(2)^(-10/7)

Now we can calculate p(10) / P0 to find the percentage as follows:

p(10) / P0 = P0(2)^(-10/7) / P0
= (2)^(-10/7)

To convert this into a percentage, we multiply by 100:

percentage = [(2)^(-10/7)] * 100

Now we can calculate:

percentage = (1.152) * 100
≈ 115.2%

Therefore, after 10 years, approximately 115.2% of the original population will be remaining.