# STEM Daily Activity: Wednesday

Throughout this week, we will be running daily competitions: every morning at 10am, we will upload that day’s activity, and anyone who sends in their answer before 9am the following day will be entered into a prize draw, with prizes awarded next week. Solutions to the puzzles will also be uploaded by 10am the following day so you can check your work.

# Wednesday: 5 August

## Exponential versus polynomial growth

In the lecture on disease modelling we talked about the exponential function 3x and derived a formula for calculating when it would ‘beat’ a polynomial function xk for some whole number k.

Q1. Calculate the smallest whole number value of x for the exponential function to ‘win’ when:

• k=5
• k=6

Q2. If we now instead consider the exponential function 2x, what is the general formula for calculating when it will ‘beat’ the polynomial function xk for some whole number k?

What is the smallest whole number value of x for the exponential 2x to ‘win’ when k=4?

## How to enter

• Complete the question above, showing the work you did to arrive at your answer
• Fill out the Competition Cover Sheet (if the document is not working for you, you can also provide the information requested in the cover sheet in the body of your email)
• Email your entry and your cover sheet to us at inspire@sjc.ox.ac.uk

## Terms & Conditions

1. All students enrolled on the Year 12 Inspire Programme are eligible to enter this competition.
2. You must complete the Competition Cover Sheet and submit it along with your entry to inspire@sjc.ox.ac.uk before the closing date. If we do not receive a completed cover sheet with your entry, we will NOT be able to consider the entry.
3. The competition closes at 9am Thursday 6 August.
4. The work you submit must be entirely your own, and should not exceed 300 words in length.
5. Competition winners will be contacted via email next week. One entry will be selected at random to win a £10 Amazon voucher and to be published on Inspire Digital.

# Tuesday’s solution

## Cannibals and hats

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