Recent studies indicate that the average surface temperature of the earth has been rising steadily. some scientists have modeled the temperature by the linear function t − 0.02t 1 8.50, where t is temperature in °c and t represents years since 1900. (a) what do the slope and t-intercept represent? (b) use the equation to predict the average global surface temperature in 2100.

a) The slope represents the change per year in the earth's surface temperature (0.02 ºC) and the T-intercept represents the average earth's surface temperature in 1900 (18.5ºC)

b) The average global surface temperature will be 22.5ºC in 2100.

Step-by-step explanation:

I think there's a "+" sign missing in the function you wrote, and that you meant to write T= 0.02t + 18.50 and I'll solve the problem for this function.

If I am wrong with the values or the + you can always substitute the values you have in your function based on the procedure I'll write down.

So, this function is T= 0.02t + 18.50.

A linear function is expressed as y = f(x) = mx + b where m is the slope of the function and b is the interception with the y-axis.

a) In this particular function, we would have that the slope of the function is 0.02 and it represents the change per year in the earth's surface temperature, since T is temperature in ºC, the change per year would be of 0.02ºC.

On the other hand, the T-intercept would be the value of the function when t=0

T(0) = 0.02(0) +18.50

T(0) = 18.50

This 18.50 represents the average surface temperature of the earth when measures started, meaning, the average surface temperature of the earth in 1900 was 18.50

b) To predict the average global surface temperature in 2100, we are going to substitute 200 in the function (since 2100 - 1900 = 200)

T(200) = 0.02 (200) + 18.50 = 4 + 18.50 = 22.5

Therefore, the average global surface temperature in 2100 will be 22.5ºC

costs the what? what is the cost of the pants?

step-by-step explanation:

if it is $10, then the price is 14.

take 40% of the cost, and then add the cost.

40% of 10 = 4

4+10 = 14.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: