Exponential Function Math Example 3

Follow the full solution, then compare it with the other examples linked below.

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A radioactive substance has a half-life of 10 years. If the initial amount is 200 g, how much remains after 30 years?

1
Use $A(t) = A_0 \cdot \left(\frac{1}{2}\right)^{t/h}$ with $A_0 = 200$ , $h = 10$ , $t = 30$ .
2
$A(30) = 200 \cdot \left(\frac{1}{2}\right)^{30/10} = 200 \cdot \left(\frac{1}{2}\right)^3 = 200 \cdot \frac{1}{8} = 25$ .

Answer

25 \text{ g}

Exponential decay uses a base between 0 and 1. The half-life formula is a special case where the base is

\frac{1}{2}

About Exponential Function

An exponential function has the form $f(x) = a \cdot b^x$ where $b > 0$ , $b \neq 1$ . The variable is in the exponent, not the base.

A bacteria population starts at 500 and doubles every 3 hours. Write an exponential model and find t

Solve [formula].

Two bacteria colonies start with 100 and 500 cells respectively. Colony A doubles every 3 hours; Col