Question

The number of species of coastal dune plants in australia decreases as the latitude, in °s, increases. There are 34 species at 11°s and 26 species at 44°s.1 (a) find a formula for the number, n, of species of coastal dune plants in australia as a linear function of the latitude, l, in °s. Round the slope to four decimal places and the intercept to two decimal places.

Answer 1

The formula for the number of species of coastal dune plants in Australia as a linear function of latitude is n = -0.2424l + 36.67. The slope is approximately -0.2424 and the y-intercept is approximately 36.67.

Step-by-step explanation:

To find a formula for the number of species of coastal dune plants in Australia as a linear function of the latitude in degrees, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, y represents the number of species of coastal dune plants, x represents the latitude in degrees, m represents the slope of the linear function, and b represents the y-intercept.

We are given two data points: (11, 34) and (44, 26). We can use these points to calculate the slope, m, using the formula m = (y2 - y1) / (x2 - x1). Let's plug in the values:

m = (26 - 34) / (44 - 11) = -8 / 33

Rounding the slope to four decimal places, we get m ≈ -0.2424. Now, let's find the y-intercept, b. We can use one of the data points, (11, 34), and the formula b = y - mx. Plugging in the values:

b = 34 - (-0.2424)(11) ≈ 36.6664

Rounding the y-intercept to two decimal places, we get b ≈ 36.67.

Therefore, the formula for the number, n, of species of coastal dune plants in Australia as a linear function of the latitude, l, in °s is n = -0.2424l + 36.67.

Answer 2

We have been given that the number of species of coastal dune plants in Australia decreases as the latitude, in °s, increases.

Further we know that there are 34 species at 11°s and 26 species at 44°s.

We can express the given information at two ordered pairs as shown below:

`(n,l)=(11,34)\text{ and }(n,l)=(44,26)`

Let us find slope of the line through these points:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))=(26-34)/(44-11)=(-8)/(33)=-0.2424`

Therefore, we can write the equation of line in slope intercept form as:

`n=-0.2424l+b`

Where b is the y intercept, and we can find its value using one of the two points.

`34=-0.2424(11)+b\\34=-2.67+b\\b=34+2.67=36.67`

Therefore, the required equation of the linear function is:

`n=-0.2424l+36.67`