1.12.4 Numerical methods in context (A-level only)

The number of users on a new social media platform was tracked over several years.

Exactly 4 years after tracking began, the number of users was 42 000.

Exactly 8 years after tracking began, the number of users was 56 000.

Given that the number of users, $U\,$ thousand, $t\,$ years after tracking began can be modelled by the equation

U^2 = a + bt^2

where $a\,$ and $b\,$ are constants,

find the value of $a\,$ and the value of $b$ .

[4]

According to the model, exactly $T\,$ years after tracking began, the number of users was 75 000.

Making your method clear,

find the value of $T$ , giving your answer to one decimal place.

(Solutions relying entirely on calculator technology are not acceptable.)

[3]

1.12.4 Numerical methods in context (A-level only) Questions