Question

1. vinny collects population data, $p(h)$, about a specific strain of bacteria over time in hours, $h$, as shown in the graph below.

exponential equations
data shown in t
t models thi
$y = 5(2)^x$
$y = 10(2)^x$
025? round your

Explanation:

Step1: Identify exponential form

The general exponential growth model is $P(h) = a(b)^h$, where $a$ is the initial value, $b$ is the growth factor, and $h$ is time in hours.

Step2: Find initial value $a$

When $h=0$, $P(0)=4$. Substitute into the model:
$4 = a(b)^0 = a(1) \implies a=4$

Step3: Find growth factor $b$

Use the point $(1,8)$: Substitute $a=4$, $h=1$, $P(h)=8$
$8 = 4(b)^1 \implies b = \frac{8}{4}=2$

Step4: Verify with other points

Check $(2,16)$: $P(2)=4(2)^2=4(4)=16$, which matches.
Check $(3,32)$: $P(3)=4(2)^3=4(8)=32$, which matches.

Answer:

$P(h)=4(2)^h$