# Exponential relationships to logarithms and straight line graph?

1. Jul 22, 2009

### JakePearson

it is suspected that cells in a sample are dividing so that the number of cells present at any one time t (measured in seconds) is growing exponentially according to the relationship y = 64 x 2^2t. it would be hard to check this relationship accurately by plotting measurements of y against t, so in practice one can use logarithms to convert it to a linear line equation. sketch a graph of log(base2)y against t, labelling the point where the graph crosses the axes?
how to i find the points on x and y axis where the line crosses, i believe the line will be a straight line, how do i do this?

I REALLY HAVE TRIED WITH THIS QUESTION, IT HAS TAKEN ME THE WHOLE DAY TO TRY AND DO, I HOPE SOMEONE CAN SHOW ME HOW TO DO THIS :)

2. Jul 22, 2009

### HallsofIvy

Staff Emeritus
What, exactly, did you spend all day doing? Taking the logarithm of both sides of $y= 64(2^{2t})$ gives $ln(y)= log(64)+ 2t log(2)$

That is of the form Y= at+ b where Y= log(y), a= 2log(2), and b= log(64). It crosses the Y axis when t= 0, at (0, ln(64)) and the t axis when Y= 0, at t= log(64)/(2log(2)).

I specifically did not give a base for the logarithm because the above is true for any base. It is particularly simple if you use, not "common" or "natural" logarithm, but the logarithm base 2: $log_2(2)= 1$ and $log_2(64)= log_2(2^6)= 6$ so Letting $Y= log_2(y)$, the equation becomes Y= 2t+ 6 with intercepts at (0, 6) and (3, 0).

3. Jul 22, 2009

### JakePearson

cheers mate, i wasnt doing that, i think i need to spend more time and concentration on logs and try a number of different questions on it, thanks again