Modeling Sugar Dissolution in Hot Water: Finding the Decay Rate

[rachael]

A spoonful of sugar is dissolving in hot water. The initial mass of the sugar was 7 grams
and 5 minutes later the mass present had halved. The mass of sugar, S grams, at time
t minutes after it was placed in the hot water can be modeled by S(t) = S0e^−kt, t ≥ 0.

b Find the exact value of k.
S0=7
therefore
i sub it in the equation where i got :
S(t)= 7e^-5k
what does S(t) equals? does it equals to 35?



thank you

 

[TD]

So the model is

$$s\left( t \right) = s\left( 0 \right)e^{ - kt}$$.

You already know s(0), that's 7. That leaves one unknown parameter, k. But you have extra information, s(5) = 3.5, let's plug this in:

$$3.5 = 7e^{ - k5}$$

Can you solve for k?

 

[rachael]

oh okai i did not read the question properly. it do not see the halving part.
thank you anywayz

 

[TD]

You're welcome