Question

It has been observed that a particular nail's growth is

directly proportional to time. When we last measured, the

nail was 3 mm and 3.5 mm exactly one week later. If the

nail continues to grow at this rate, determine the function

that represents the nail's growth and graph it.

Answer 1

NOTE: I have made this explaination long so that you understand it as some people view my answers too short or without enough info. feedback would be nice.

If The growth is directly proportional this means that the graph will be linear.

For simplicity and since the question does not specify, we will make one time unit one week.

Our base function is "F(t) = mt + b"  with F(t) being the length of nail with respect to time.
[This is just mx + b]

so F(t)  = mt + b

We will assume that when t = 0, we have 3mm of nail. So...

F(0)  = 3
3  = m(0) + b
b = 3

F(t)  = mt + 3
To find slope we can sub when F(t) is 1

F(1)  = 3.5
3.5  = m + 3
m = 0.5 = $\frac{1}{2}$

Our Equation is:

"F(t)  = $\frac{1}{2}$ t + 3

Use a graphing calculator, an online grapher, or pen and paper for your graph.

Brainest answer is appreciated.