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
great! the y-intercept is correct at (0, 23). now for your second point, whats the growth factor when the epidemic increases by 10% per week? use that to find the function value at t = 1

Explanation:

Step1: Define growth function form

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

Step2: Plug in given values

$N_0=23$, $r=0.10$, so $N(t)=23(1+0.10)^t = 23(1.1)^t$.

Step3: Find t=1 value

Substitute $t=1$: $N(1)=23\times1.1 = 25.3$.

Step4: Identify key points

Y-intercept: $(0, 23)$; Second point: $(1, 25.3)$. Plot these and draw the exponential curve passing through them, increasing over time.

Answer:

The exponential function is $N(t)=23(1.1)^t$. The graph has a y-intercept at $(0, 23)$, passes through $(1, 25.3)$, and is an upward-sloping exponential curve showing increasing infected victims over weeks.