Question

A scientist cools some water at a constant rate. the graph and table show how the temperature of the water changes with time.

Answer 1

Answer:

C

Step-by-step explanation:

The easiest way to determine this is to realize that time is the independent variable (n) and temperature is the dependent variable (a).

From the table, we can plug in the two points (n) into n of each equation and see if that equals the temperature values (a).

A little thinking would get us to plug the numbers in C first.

$a(n)=46-(n-1)*4\\46-(5-1)*4=30$

Works!!

Now, second number:

$a(n)=46-(n-1)*4\\46-(6-1)*4=26$

Works!!

Hence, C is the correct answer.

Answer 2

Answer:

$a(n)=46-(n-1) \times 4$

Step-by-step explanation:

It's important to know that the graph is showing a linear function, which means its equation cannot be exponential. So, choices A and B are not correct here.

To find the correct equation, we could find the slope first with the following formula and the two given points

$m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }\\ m=\frac{26-30}{6-5}=4$

Now, we use the point-slope formula to find the equation

$y-y_{1} =m(x-x_{1} )\\y-30=4(x-5)\\y=4x-20+30\\y=4x+10$

Notice that choice C has the same coefficient of 4, which is the slope of the line. Therefore, that's the right answer.

Let's prove it for $n=6$

$a(n)=46-(n-1) \times 4\\a(6)=46-(6-1) \times 4=46-20=26$

As the table shows.

Therefore, choice C is correct.