Question

Help me with this weird question!!

A tumor in a rat responds to a new radiation treatment by shrinking 5% with each treatment. How many treatments before the tumor has shrunk to a quarter of its original size?

HINT: The size of the tumor doesn't matter.

Answer 1

a) approximately 38 treatments
b) approximately 11 treatments
c) approximately 27 treatments
d) approximately 75 treatments

Answer 2

Well, a quarter is how much percent?

Answer 3

25%

Answer 4

So, if the treatment is increasing by 5% each time, it would 5 treatments, 5 x 5 is 25, right? But that's not one of the answers...

Answer 5

oh no

Answer 6

\[(0.5)^n = 0.25\]

Find n.

Answer 7

ack

0.05

Answer 8

to decrease a number by \(5\%\) multiply it by \(100\%-5\%=95\%=.95\)

Answer 9

it has to shrink 75% to get to a quarter..

Answer 10

your job is to solve
\[.95^x=.25\]

Answer 11

Ack, yeah. Listen to satellite. Sorry. Misread the question slightly.

Answer 12

I misread the question as well.
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Answer 13

for this you need logarithms
by the change of base formula if
\[.95^x=.25\] then
\[x=\frac{\ln(.25)}{\ln(.95)}\] and a calculator

Answer 14

if you have not got to logs get, then you can guess and check which number \(x\) gives you \[.95^x=.25\]

Answer 15

Ooooh!! 27?

Answer 16

that is what i get, yes

Answer 17

thank you all :)