Exponential Functions & Logarithms (AQA Level 3 Mathematical Studies (Core Maths): Paper 2C: Graphical Techniques): Revision Note

Remembering a simple numerical example such as:

$2^3=8$ so ${\log }_2\left(8\right)=3$

can be a really useful reminder for how logarithms work.

A marketing company who work with an online video platform suggest that the number of views for a particular "viral" video can be modelled with the following equation:

$V=1.{56}^t$

where $V$ is the number of views, and $t$ is the time in hours since the video was published.

(a) Estimate the number of views, to the nearest 10, after 24 hours according to the model.

Answer:

Substitute in $t=24$

$V=1.{56}^{24}=43150.9499...$

Round to nearest 10

43 150 views

(b) Estimate the number of hours taken for the video to reach 1 million views according to the model. State your answer to the nearest hour.

Answer:

Substitute in $V=1000000$

$1000000=1.{56}^t$

Use the relationship:
If $a=b^x$ then ${\log }_{b}a=x$
to rewrite as a logarithm

${\log }_{1.56}\left(1000000\right)=t$

Type the logarithm into your calculator

$t=31.06802578...$

Round to nearest hour

31 hours