Help with logarithms

Question

An economist has found the following function for the number of mobile phones (in millions) sold worldwide since the year 2014:

V(t) = 1244.74 · 1.1439t

t= time in years. t=0 is the year 2014

Compute algebraically in which year 3.5 billion mobile phones will be sold worldwide according to this function.

Can someone explain to me how to calculate this algebraically step by step? I have an exam tomorrow and my log skills are still rusty....

Thank you.

Answer 1

I assume the t is supposed to be an exponent:

 

V(t) = 1244.74 · 1.1439^t

 

Also it appears that V(t) is in units of millions of cell phones.  3.5 billion, then, will be 3500 million.

 

3500 = 1244.74· 1.1439^t

3500/1244.74 = 1.1439^t

 

To get the t out of the exponent, use logs:

 

log(3500/1244.74) = log(1.1439^t)

log(3500/1244.74) = t·log(1.1439)      [Log property: log(a^b) = b log(a)]

log(3500/1244.74)/log(1.1439)  = t

 

Use your calculator to compute t.  You can use any base log.  Add t to 2014 to get the year (drop the decimals).