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 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
growth factor: 1.1
yes, the growth factor is 1.1! now its 23 times 1.1, that gives you the number of victims at t = 1. also, your y-intercept means it should stay at 23.
function: n(t)=23(1.1)^t
perfect function! now adjust your graph to match it. first, move the y-intercept point to 23. then calculate 23 × 1.1 to find the value at t = 1, and plot that point.
value at t=1:25.30 (or if rounding to whole numbers, 25)
excellent calculation! now adjust your graph: drag the y-intercept point to 23, and move your second point to (1,25). your math is correct--just need to adjust the graph to match.
ready

Explanation:

Step1: Define growth rate & initial value

Initial victims $N_0=23$, growth rate $r=0.10$

Step2: Write exponential growth formula

Exponential growth function: $N(t) = N_0(1+r)^t$

Step3: Substitute values into formula

$N(t) = 23(1+0.10)^t = 23(1.1)^t$

Step4: Calculate value at $t=1$

$N(1) = 23\times1.1 = 25.3$

Answer:

The exponential function is $N(t)=23(1.1)^t$. The value at $t=1$ is 25.3, so the graph should pass through $(0, 23)$ and $(1, 25.3)$ to match the function.