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1.5.14 Convert between cartesian and parametric forms (A-level only)

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Question 45

A marine biologist is monitoring the environmental conditions of a coastal pool. The temperature TTT (in degrees Celsius) and the salinity SSS (in g/L) of the pool at time ttt hours after high tide are modeled by the parametric equations

T=3t+2,S=4t+32t+1,t>0 T = \frac{3}{t} + 2, \quad S = \frac{4t + 3}{2t + 1}, \quad t > 0 T=t3​+2,S=2t+14t+3​,t>0
a.

Show that the relationship between salinity and temperature can be written in the form S=g(T)S = g(T)S=g(T), where ggg is the function

g(T)=aT+bcT+d,T>k g(T) = \frac{aT + b}{cT + d}, \quad T > k g(T)=cT+daT+b​,T>k

and a,b,c,da, b, c, da,b,c,d, and kkk are integers to be found.

[5]
b.

Hence, or otherwise, state the range of ggg.

[2]

1.5.14 Convert between cartesian and parametric forms (A-level only) Questions

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