Higher November 2022 Paper 4 Q14
14 An estimate for the number of seals on an island is given by the formula
\[P = 5200 \times 1.02^t\]where \(P\) is the number of seals \(t\) years after the start of year 2015.
(a) Write down the annual percentage increase in the number of seals on the island. [1]
(b) Use the formula to show that there may have been about 4700 seals on the island at the start of year 2010. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 2[%] | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 5200 ÷ \(1.02^5\) oe 4709 to 4710 | 2 | M1 for 5200 ÷ \(1.02^k\) or 4700 × \(1.02^5\) or 5200 = \(n\) × \(1.02^5\) | equivalent is 5200 × \(1.02^{-5}\) condone : 4700 × \(1.02^5\) = 5189 to 5190 for 2 marks accept 1.104… for \(1.02^5\) and 0.9057… for \(1.02^{-5}\) |