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
good! 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: Identify growth factor

A 10% weekly increase means the growth factor is $1 + 0.10 = 1.1$.

Step2: Define exponential function

Use initial value $23$, growth factor $1.1$. The general form is $N(t) = N_0 \times (growth\ factor)^t$.
Expression: $N(t) = 23 \times 1.1^t$

Step3: Find value at $t=1$

Substitute $t=1$ into the function.
Expression: $N(1) = 23 \times 1.1^1 = 25.3$

Answer:

Growth factor: $1.1$
Function: $N(t) = 23(1.1)^t$
Value at $t=1$: $25.3$ (or 25 if rounding to whole people)