A household budgeting app models monthly savings, in pounds, as \(S = \dfrac{t^{2}-9}{t-3}\), for \(t \gt 3\), where \(t\) is the number of months since the...
Question 1 Report
A household budgeting app models monthly savings, in pounds, as \(S = \dfrac{t^{2}-9}{t-3}\), for \(t \gt 3\), where \(t\) is the number of months since the account opened.
- Simplify \(S\) fully by factorising the numerator. (2)
- Using the simplified form, work out \(S\) when \(t=9\). (1)
- The app adds a fixed joining bonus of \(\pounds15\) to \(S\). Write an expression for the total amount \(T(t)\), in its simplest form. (1)
- The household wants \(T(t)=50\). Solve to find \(t\). (2)
- State, with a reason, whether this value of \(t\) is realistic within a 2-year (24-month) savings plan. (1)
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