Question

the number of victims of a flu epidemic increases at a rate of 10% per week. there are currently 23 people infected. graph the exponential function that represents the number of victims after $t$ weeks.
show your work here

Explanation:

Step1: Define exponential growth formula

The general exponential growth function is $N(t) = N_0(1+r)^t$, where $N_0$ is the initial number, $r$ is the growth rate, and $t$ is time.

Step2: Substitute given values

Here, $N_0=23$, $r=0.10$. So the function is:
$N(t) = 23(1+0.10)^t = 23(1.10)^t$

Step3: Calculate key points for graphing

• At $t=0$: $N(0)=23(1.10)^0=23$
• At $t=1$: $N(1)=23(1.10)^1=25.3$
• At $t=2$: $N(2)=23(1.10)^2=27.83$
• At $t=3$: $N(3)=23(1.10)^3=30.613$

Step4: Plot points and draw curve

Plot $(0,23)$, $(1,25.3)$, $(2,27.83)$, $(3,30.613)$ on the grid, then draw a smooth increasing curve through them, starting at $(0,23)$ and rising as $t$ increases.

Answer:

The exponential function is $N(t)=23(1.10)^t$. The graph is a smooth increasing curve passing through the points $(0,23)$, $(1,25.3)$, $(2,27.83)$, $(3,30.613)$, with the horizontal axis representing weeks $t$ and the vertical axis representing the number of infected victims.