- #1

Theodore Hodson

- 24

- 0

## Homework Statement

These questions require you to see a graph - which can be accessed from the link below

43.

a). Find the growth factor between the numbers of stick insects in consecutive time intervals of two weeks. Hence find a relationship between ##x## (time in days) and ##y## (number of insects) that can be used as an approximate model for the data given in the graph.

b). Use the model to estimate

i) the number of insects 45 days after the first recorded entry on the graph

ii) how many days after the first recorded entry the number of insects had grown to 100.

Explain why these results can only be estimates.

c). Find the rate at which the numbers are growing 10 weeks after the first entry and comment on the accuracy of the result.

## Homework Equations

http://ibin.co/27ygaCJx9Hyx - link to the image of the graph

## The Attempt at a Solution

Okay so I'm stuck on the part 'a' of this problem - I need to get that sorted before I move on to part b and part c.

I figured out that the two week growth factor would be approximately ##1.5## because from the graph the number of stick insects grows from ##10## to ##15## in a two week period.

I then presume that the question wants me to find an equation in the form ##y=ab^x## that will describe what's happening in the graph but in terms of days instead of weeks. From the points on the graph, I've tried setting up a system of equations to solve for ##a## and ##b## but I reckon I'm barking up the wrong tree as the textbook gives the answer as ##y=6.7(15^\frac{x}{14})## and I'm not sure how to get that answer. Would be very pleased if anyone can give me some pointers in the right direction :)

Thanking you