Question

Insulin is used to regulate sugar in the bloodstream. A dose of 10 units breaks down by about 5% each minute after injection. How long does it take for the remaining insulin to be half of the original dose? Round to the nearest tenth.

Answer 1

Answer:

Explanation:

• The initial dose of the Insulin = 10 Units

The insulin breaks down by about 5% each minute, therefore:

• The decay rate, r= 5%

We want to determine the time it will take for the remaining dosage to be half (5 units) of the original dose.

We use the exponential decay function:

$N(t)=N_o(1-r)^t$

Substituting the given values, we have:

$\begin{gathered} 5=10(1-0.05)^t \\ \frac{5}{10}=0.95^t \\ 0.5=0.95^t \end{gathered}$

To solve for t, we change to logarithm form.