Stuck on exponential modelling question where the initial value isnt given

Spent ages trying to solve this question in various ways but to no avail-pls help

Q: https://imgur.com/a/ukvT56B

The ms is given but I still don’t get it

Reply 1

mqb2766

Original post by rhyso4

Spent ages trying to solve this question in various ways but to no avail-pls help

Q: https://imgur.com/a/ukvT56B

The ms is given but I still don’t get it

You could solve it as a geometric sequence (determine a and r) or by finding the parameters of an exponential function.(so Aexp(kt)). What have you tried to do?

Reply 2

Lebkuchen

Original post by rhyso4

Spent ages trying to solve this question in various ways but to no avail-pls help

Q: https://imgur.com/a/ukvT56B

The ms is given but I still don’t get it

hi couldn't you try ky=ae^kt
and do a simultaneous equation
can find k
substitute - find A
substitute following
if there is another way can you send the mark scheme so I can try find out what they have done

Reply 3

DFranklin

Original post by Lebkuchen

There's a fairly obvious "basic arithmetic" solution to this (obvious enough that it's hard to hint at it without giving it away).

But I can give a "link" with the exponential approach:

The general form for exponential modelling is

y = ae^{kt}

(where a, k are constants). If we write

k = p/q

(where p, q are new constants), we get:

y = a e^{pt/q} = a (e^p)^{t/q} = aG^{t/q}

, where

G = e^p

.

Looking at the question, there are some fairly obvious choices for G and q that will make everything work nicely (i.e. with nice simple numbers and no need for a calculator).