We can use the given formula for the rate of change of the weight of the solid to estimate the amount of solid 1 second later.
If there is 6 grams of solid at time t, then f(t) = 6 g.
To estimate the amount of solid 1 second later, we can use the derivative formula:
f'(t) = −2f(t)(5+ f(t))
We want to estimate the value of f(t+1), which represents the weight of the solid 1 second later.
To do this, we can use Euler's method, which is an approximation method for solving differential equations.
Euler's method uses the formula:
f(t+1) ≈ f(t) + f'(t)Δt
where Δt is the time step (in minutes).
Since we want to estimate the amount of solid 1 second later, we can set Δt = 1 minute.
Plugging in the values for f(t) and f'(t), we get:
f(t+1) ≈ f(t) + f'(t)Δt
f(t+1) ≈ 6 - 2(6)(5+6)
f(t+1) ≈ -66
Therefore, the estimated weight of the solid 1 second later is -66 grams. However, this result does not make physical sense since weight cannot be negative.
It is possible that the given formula for f'(t) does not accurately describe the behavior of the solid, or that there was an error in the calculation.
or maybe im just bad at maths