Help with this Question

[Jm23]

Guys, please see the attached picture. I am stuck on part (iv) of this question with regards to modelling curves. I know that the value of a = 0.985, but cannot work out how k = 3,400,000. I got 3,200,000. I have checked my table and graph against the answers and they are identical.

My working for k:

y intercept = ln k = 14.98
k = e^14.98
k = 3200000

 

[Dr.Peterson]

In my work I kept everything in terms of thousands as in the table, but I got the same result you have, k = e^14.98.

Since they base this on drawing a line and estimating its slope and intercept, maybe they drew it differently. Mine goes through the point at t=0, so of course the intercept should correspond to the initial number, 3,200,000! I made my graph on Excel, which puts it at 3,240,000, not nearly 3,400,000.

Can you show their complete answer?

 

[Jm23]

Hi, the answers are here - q5

 

[Dr.Peterson]

It would appear that they drew a graph whose intercept is a little above 15 (the best fit line on Excel has 14.991, a little below 15, so their line must be hand drawn as they asked you to do); if they called it 15.0 they'd get k = 3,269,000, which wouldn't round to 3,400,000, so they must have called it something like 15.04.

The important thing to learn is that slight differences in your intercept can make noticeable differences in you answer, so you shouldn't let small differences such as you found make you think you (or they) are wrong. The problem involves a subjective element, so you can expect differences.

 

[Jm23]

Ah that makes sense. Thank you very much for your help.