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 23×1.1 to get 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 (25 if rounding to whole people)
excellent calculation! now update 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.
reply:

Explanation:

Step1: Identify initial value

Initial number of victims $N_0 = 23$

Step2: Determine growth factor

Growth rate = 10% = 0.1, so growth factor $r = 1 + 0.1 = 1.1$

Step3: Write exponential function

Exponential growth formula: $N(t) = N_0 \times r^t$
Substitute values: $N(t) = 23(1.1)^t$

Step4: Calculate value at $t=1$

Substitute $t=1$: $N(1) = 23 \times 1.1 = 25.3$
Round to whole number: $25$

Answer:

The exponential function is $N(t)=23(1.1)^t$. The value at $t=1$ is 25, so the graph should pass through the points $(0, 23)$ and $(1, 25)$.