Zadanie 2c, Paper 2, maj 2023, TZ1, Matematyka AA IB SL
Wzorowane na: Matematyka AA IB SL — maj 2023, TZ1, Paper 2 (zadania wzorowane), pytanie 2(c). Treść, dane i kontekst są zmienione; sprawdzane umiejętności, format i punktacja jak w oryginale.
Darmowe konto pozwoli wrócić do niego później.
Zadanie
Wspólne informacje do wiązki zadań
A fictional workshop machine has resale value C(t) = 56000(0.88)t dollars, where t is years after 1 January 2023. On that date a cooperative deposits 20000 dollars in an account earning 4% interest compounded annually. No further transactions occur. It plans to buy the machine at its modelled resale value on 1 January 2029.
Polecenie
How much additional money is needed beyond the account balance on that date?
Korepetytor
Nie wiesz, jak ruszyć? Korepetytor zna to zadanie i poprowadzi Cię krok po kroku, bez gotowca.
3 rozmowy · bez karty · Zaloguj się
Sprawdź się
Jak poszło?
Pokaż rozwiązanieUkryj rozwiązanie
Odpowiedź z klucza
The balance is 20000(1.04)^6=25306.38036992 dollars. The shortfall is 26006.628859904−25306.38036992=700.248489984 dollars, approximately 700 dollars (three significant figures), or 700.25 dollars to cents.
Schemat punktowania
A1:correct compound-interest calculation or financial-app inputs. M1:subtract their account balance from their machine value. A1:700 dollars to three significant figures, or 700.25 dollars to cents. Follow through their part (b) value; use of the accepted three-significant-figure value 26000 with unrounded balance gives 693.61963008…, so 694 dollars is also accepted when this calculation is shown.
Komentarz. Paper 2: calculator and AA SL formula booklet allowed. Retain intermediate precision; give three significant figures unless an exact answer is requested.