59, 24 rabbits were released into the wild in Australia, where they had no natural predators. Their population grew exponentially, doubling every 6 months. (a) Determine P(t), the function that gives the population at time t, and the differential equation describing the population growth. Let units for t be years.

The function that gives the population at time t is:

Step-by-step explanation:

In 1859 (t = 0) the population of rabbits in the wilds of Australia was P (0) = 24.

Consider P (t) as the population of rabbits at time t.

It is provided that the population of rabbits grew exponentially.

The formula representing the exponential growth is:

Here,

A₀ = initial value

a = growth rate

t = time.

The formula representing the exponential growth of rabbits in the wilds of Australia is:

It is provided that P (0) = 24.

It is provided that every 6 months the population of rabbits double.

Then after half a year the population is 48.

Compute the value of a as follows:

The function that gives the population at time t is:

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

50-38=12

step-by-step explanation: