Zadanie 1a
Find its initial temperature.
Exponential and logarithmic functions
Connect exponential and logarithmic graphs, inverse relationships and parameters in mathematical models.
Tę umiejętność sprawdzają 33 zadania wzorowane na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 33 Otwórz w wyszukiwarce z filtrami
Zadanie 1b
Find its temperature after 12 minutes.
Zadanie 1c
State the ambient temperature predicted by the model.
Zadanie 3a
State the initial reading.
Zadanie 3b
Find k.
Zadanie 3c
When does the reading reach 16°C?
Zadanie 9b
State (i) a; (ii) b.
- Materiał graficzny
Zadanie 9c
Find the exact x-coordinates where f(x) = 0.
Zadanie 9d
The maximum value of f is 2. Find k.
Zadanie 7c
(i) Write Fund B’s balance after n years in the form 6000qⁿ. (ii) Find the smallest number of complete years after which Fund B exceeds Fund A.
Zadanie 8a
Estimate the number of accounts after one year using F.
Zadanie 8b
Find the first complete month when F predicts at least 28000 accounts.
Zadanie 8c
Write F(t)=2400eᵏᵗ. Find k exactly.
Zadanie 8e
Find A in the finite-market model.
Zadanie 8g
Give one reason why G is more suitable than F for long-term adoption in a finite local market.
Zadanie 9a
Find the coordinates of (i) P; (ii) R.
- Materiał graficzny
Zadanie 7a
Show that f−1(x) = 2 + ln(4x/5).
Zadanie 7d
Solve f(x)=g(x), giving x in the form a+ln b with rational a,b.
Zadanie 6
The function h(x) = log2(5x2 − rx + 2r − 3) must be real-valued for every real x. Find all possible r.
Zadanie 6
The expression h(x) = log3(3x2 − rx + r − 2) must define a real-valued function for every real x. Find all possible real r.
Zadanie 8c
Using B, (i) predict capacity in 2082; (ii) interpret 1.022.
Zadanie 8d
Use C to predict capacity in 2082.
Zadanie 8c
Using B: (i) predict capacity in 2080; (ii) interpret 1.025.
Zadanie 8d
Use C to predict capacity in 2080.
Zadanie 3a
State the initial brightness.
Zadanie 3b
Find k.
Zadanie 3c
Find T.
Zadanie 5
Find all real k for which e2x + ln k = 4ex has at least one real solution x.
Zadanie 7a
Find (i) the initial temperature; (ii) the temperature after four minutes.
Zadanie 7e
Find the constant enclosure temperature approached by the chamber.
Zadanie 8a
State the vertical asymptote of g.
Zadanie 8a
State the vertical asymptote of g.
Zadanie 5
A collection of unprocessed archival files shrinks according to N(t) = 24000ekt, k<0, where t is the number of years after 1 January 2017. By 1 January 2023,14% of the initial files had been processed. Estimate the number remaining on 1 January 2036.