Question

Please help

A population’s instantaneous growth rate is the rate at which it grows for every instant in time. Function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.

Answer 1

Function r has two complex zeros and one real zero. Based on the instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.

Step-by-step explanation: I got it right

Answer 2

Given:

The function is

`r(x)=0.05(x^2+1)(x-6)`

where, function r gives the instantaneous growth rate of a fruit fly population x days after the start of an experiment.

To find:

Number of complex and real zeros.

Time intervals for which the population increased and population deceased.

Solution:

We have,

`r(x)=0.05(x^2+1)(x-6)`

`r(x)=0.05(x^3+x-6x^2-6)`

Here, degree of function x is 3. It means, the given function has 3 zeros.

From the given graph it is clear that, the graph of function r(x) intersect x-axis at once.

So, the given function r(x) has only one real root and other two real roots are complex.

Therefore, function r has 2 complex zeros and one real zero.

Before x=6, the graph of r(x) is below the x-axis and after that the graph of r(x) is above the x-axis.

Negative values of r(x) represents the decrease in population and positive value of r(x) represents the increase in population.

Therefore, based on instantaneous growth rate, the population decreased between 0 and 6 hours and the population increased after 6 hours.