Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths OCR (MEI)
  5. Question bank

1.9.10 Differentiate e^kx, a^kx and ln x (A-level only)

EasyMedium
1234567891011121314
Question 11

The concentration of a chemical reactant in a solution, CCC mg/L, after ttt minutes is modeled by the equation:

log⁡10C=1.84−0.072t \log_{10} C = 1.84 - 0.072t log10​C=1.84−0.072t
a.

Show that this equation can be written in the form C=km−tC = km^{-t}C=km−t, where kkk and mmm are constants. Give the value of kkk to the nearest whole number and the value of mmm to 2 significant figures.

[3]
b.

With reference to the equation in part (a), interpret the value of the constant kkk.

[1]
c.

When the reaction temperature is increased, the concentration CCC after ttt minutes satisfies the equation:

C=560×1.15−t C = 560 \times 1.15^{-t} C=560×1.15−t

Use calculus to find, to 2 significant figures, the value of dCdt\frac{dC}{dt}dtdC​ when t=4t = 4t=4.

[3]

1.9.10 Differentiate e^kx, a^kx and ln x (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.9.10 Differentiate e^kx, a^kx and ln x (A-level only)