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IB Maths AA SL 2.10 Solving Equations

IB Maths AA SL 2.10 Solving Equations
IB Mathematics: analysis and approaches guide, first assessment 2021

Practise solving equations and inequalities analytically or graphically, selecting technology when needed and interpreting intersections, thresholds and contextual solutions.

How this is tested

  • equate two function rules to obtain an equation whose roots give their intersection coordinates
  • choose an algebraic, graphical or numerical method appropriate to the form of the equation
  • apply domain or contextual restrictions and report only solutions valid for the original problem

Question 8

[Maximum number: 7]

A population of frogs, F, in a swamp after t months, can be modelled by the function

F(t)=1850×1.105t where t≥0F(t)=1850 \times 1.105^{t} \text { where } t \geq 0

Question 8(a)

(a)

Find the population of frogs after one year.

[ 2 ]

Question 8(b)

(b)

After x complete months, the population will be at least 35000 frogs. Find the value of x The function F can be written in the form F(t)=1850ektF(t)=1850 \mathrm{e}^{k t}.

[ 3 ]

Question 8(e)

(c)

After 15 months, this model predicts a population of 6995 frogs. Find the value of A.

[ 2 ]