solving variable in exponential equation

i am trying to use the equation: y = ae^rt; to solve for t; y = final population, a = initial population, r = rate increasing. i'm using editor but it is not working. i know the answer to my equation is around 210, however my code below is not working:

sysm y a r t 
y == a * ((exp((r*t));
a = 300;
r = .10;
y = 600;
solve t 

[SP]

getting this error when running it after putting it in editor

Error: File: untitled Line: 2 Column: 22

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

[madhan ravi]

syms y a r t 
eqn=y == a * exp((r*t));
t=solve(eqn,t);
a = 600;
r = .10;
y = 600;
Final_t=subs(t)

Yields:

t =
 
log(y/a)/r %-> log(600/600)/r==>0 , so why do you say 210?

[SP]

when you actually solve the math using the eqaution on paper, the correct answer is 208:

https://media.cheggcdn.com/media%2F995%2F99590c89-d908-494f-88e3-15398f2d22da%2FphpUc0no0.png

so your code must be wrong since t is suppose to equal about 208

[madhan ravi]

what's r ? it's not there in the picture.

[Walter Roberson]

The paper uses values around 300 that are no-where to be found in the 600-ish values you posted.

[SP]

i apoligize a = 300, that was my mistake

Answer 1

[KSSV]

syms y a r t 
eqn = y == a * ((exp((r*t))));

S = solve(eqn,t) ;

a = 600;
r = .10;
y = 600;

S = subs(S,a) ;
S = subs(S,r) ;
S = subs(S,y) ;

Answer 2

[Stephan]

syms t
a = 600;
r = .10;
y = 600;
eq = y - a * (exp(r*t)) == 0;
tsol = solve(eq,t)

[SP]

error:

Undefined function or variable 'y'.

[SP]

this worked, however when i enter, i get this:

tsol =

log(y/a)/r

how can i can the actual number value, the anser in terms of variables is right, but i am looking for a number

[Stephan]

error is corrected. the solution is zero. this is obviously.

[Stephan]

use

clear a y r t