Question

module 11 (linear equations) assignment
score: 18/20 answered: 18/20
question 19
scientists know that the average surface temperature of the world has been rising steadily. one model found using sets of temperature data is.
t = 0.02t + 15.0
where t is temperature in ^circ c and t is years since 1950.
(a) what is the slope and y - intercept?
slope =

y - intercept =

(b) use the equation to predict the average global surface temperature in 2039. round to nearest degree.
t =
^circ c
submit question

Explanation:

Part (a)

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. In the given equation \(T=0.02t + 15.0\), we can compare it with the slope - intercept form (where \(T\) is like \(y\) and \(t\) is like \(x\)).

Step2: Identify slope and y - intercept

For the equation \(T = 0.02t+15.0\), by comparing with \(y=mx + b\), the coefficient of \(t\) (which is the independent variable, similar to \(x\) in the slope - intercept form) is the slope. So the slope \(m = 0.02\). The constant term is the \(y\) - intercept (or in this case, the \(T\) - intercept when \(t = 0\)). So the \(y\) - intercept \(b=15.0\).

Part (b)

Step1: Calculate the value of \(t\)

We need to find the temperature in 2039. Since \(t\) is the number of years since 1950, we calculate \(t=2039 - 1950=89\).

Step2: Substitute \(t = 89\) into the equation

We substitute \(t = 89\) into the equation \(T=0.02t + 15.0\). So \(T=0.02\times89+15.0\). First, calculate \(0.02\times89 = 1.78\). Then, \(T=1.78 + 15.0=16.78\).

Step3: Round to the nearest degree

Rounding \(16.78\) to the nearest degree, we get \(T\approx17\).

Answer:

(a) Slope \(=\boldsymbol{0.02}\), y - intercept \(=\boldsymbol{15.0}\)

(b) \(T=\boldsymbol{17}\) \(^{\circ}\text{C}\)