Exponential Function Math Example 1

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

easy

A bacteria population starts at 500 and doubles every 3 hours. Write an exponential model and find the population after 9 hours.

1
The general form is $P(t) = P_0 \cdot b^{t/k}$ where $P_0 = 500$ , $b = 2$ , and $k = 3$ .
2
Model: $P(t) = 500 \cdot 2^{t/3}$ .
3
At $t = 9$ : $P(9) = 500 \cdot 2^{9/3} = 500 \cdot 2^3 = 500 \cdot 8 = 4000$ .

Answer

P(9) = 4000

Exponential growth models use the form

P_0 \cdot b^{t/k}

where

b > 1

represents growth. The ratio

t/k

counts how many doubling periods have elapsed.

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.

Solve [formula].

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

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