r' = 2.1/(t+5)
r = 2.1 log(t+5) + C
at t=0,
3.8 = 2.1 log5 + C
C = 3.8-2.1log5 = 0.42
so,
r = 2.1 log(t+5)+0.42
now just plug in t=27
At a summer campfire, the radius of a marshmallow on a stick expands at the rate of
\ {r ' (t)} = \frac{2.1 }{1 t + 5} mm/s
where t is the time of heating in seconds. Initially the radius was 3.8 mm. Find the radius after 27 seconds using the following steps:
When substituting, du = dt
The resulting integral looks like \int \frac{A}{u} \, du where A is a numerical value.
A =
The constant of integration, C is
The radius after 27 seconds is
mm
1 answer