Question

The number of flies on the farm is growing exponentially. In 2011 there were 75 flies. In 2017 there were 1300 flies. Write the equation representing the population P of flies over time t.

Round your number to 4 decimal places.

Answer 1

The equation representing the population P of flies over time t is P = 75 * e^(t * ln(17.3333)/6).

Step-by-step explanation:

To represent the population P of flies over time t, we can use the exponential growth equation.

The general form of the equation is P = P0 * e^(rt), where P0 is the initial population, e is the base of the natural logarithm, r is the growth rate, and t is the time.

In this case, we are given the values P0 = 75 (in 2011) and P = 1300 (in 2017).

We can plug these values into the equation to find the growth rate r:

1300 = 75 * e^(6r)

e^(6r) = 1300/75

e^(6r) = 17.3333

Take the natural logarithm of both sides:

ln(e^(6r)) = ln(17.3333)

6r = ln(17.3333)

r = ln(17.3333)/6

Now we have the value of r. The equation representing the population P of flies over time t is:

P = 75 * e^(t * ln(17.3333)/6)