Zadanie 3a
State the initial reading.
Exponential and logarithmic functions
Connect exponential and logarithmic graphs, inverse relationships and parameters in mathematical models.
Tę umiejętność sprawdza 17 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 17 Otwórz w wyszukiwarce z filtrami
Zadanie 3b
Find k.
Zadanie 3c
When does the reading reach 16°C?
Zadanie 12d
Find the long-term limiting number of active sensors.
Zadanie 2a
For the logistic model: (i) interpret choosing L=1000; (ii) find C; (iii) find k; (iv) predict the membership count at t=8, to the nearest whole member.
Zadanie 2b
For the Gompertz model: (i) state dx/dt at x=1000; (ii) interpret it; (iii) for h(x) = ln(ln 1000 − ln x),0<x<1000, show h′(x) = −1/[xln(1000/x)]; (iv) hence separate variables to show ln x = ln 1000 − Ae−at with A>0; (v) find A as ln p for a positive…
Zadanie 2c
Compare the two predictions with the t=8 audit.
Zadanie 5
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 10c
Using B: (i) predict capacity in 2080; (ii) interpret 1.025.
Zadanie 10d
Use C to predict capacity in 2080.
Zadanie 1a
On common axes, sketch y = log2 x, y = log10 x and y = x2 + e2 for x>0. Label all three graphs and state the nonzero x-intercept.
Zadanie 1d
Investigate representative graphs. State the number of intersections in each base range: (i) 0<a<1; (ii) 1<a<1.05; (iii) 1.1<a<2.
Zadanie 1f
Give the exact sets of bases for which the graphs have (i) two intersections; (ii) no intersections. You may use the unique contact base a∗ = exp(1/(2e2)).
Zadanie 4
Find all real k for which e2x + ln k = 4ex has at least one real solution x.
Zadanie 10a
State the vertical asymptote of g.
Zadanie 10a
State the vertical asymptote of g.
Zadanie 4
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.