Question

1. the number of newborn babies in a city increases by 4% every year. if there are 600 newborns today, what will the number of newborns be in 3 years?

a. $600(0.04)$ b. $600(1.04)$ c. $600(1.04)(3)$ d. $600(1.04)^3$
show your work:

1. which function goes down 12% when x goes up by 1?

a. $f(x)=0.12^x$ b. $f(x)=0.88^x$ c. $f(x)=12^x$ d. $f(x)=88^x$
show your work:

1. the function $c(x)=22(1.04)^x$ models the cost in dollars of a scientific calculator used in a school. $x$ represents the number of years since 2015.

a. does the cost of the calculator increase (grow) or decrease (decay) over time? (circle one)
b. by what percentage does it increase or decrease?
c. how much does an ounce of calculator cost in 2026? show your calculation.
help: 2020 is 5 years since 2015.

1. benadryl is a medicine for allergies. it helps if someone has sneezing, runny nose, or itchy eyes, where $x$ is the number of hours since the person took the medicine. $y = 25(0.76)^x$

a. in the equation, what does the 25 tell us about the situation?
b. does the 0.76 show exponential growth or exponential decay? share your thoughts!
c. use the equation to calculate how much benadryl left after 3 hours. left=remains

Explanation:

Step1: Identify growth formula

The number follows exponential growth: $N = N_0(1+r)^t$, where $N_0=600$, $r=0.04$, $t=3$.

Step2: Substitute values

$N = 600(1+0.04)^3 = 600(1.04)^3$

Step1: Find decay factor

A 12% decrease means $1-0.12=0.88$.

Step2: Match to function

The decay function is $f(x)=0.88^x$.

a. The function has a base greater than 1 ($1.04>1$), which indicates exponential growth.
b. The base is $1.04$, so the growth percentage is $1.04-1=0.04$, or 4%.
c. First calculate $x$: 2026-2015=11. Substitute $x=11$ into the cost function.

a. In the exponential model $y = a(b)^x$, $a$ is the initial value when $x=0$ (time 0, right after taking the medicine).
b. Exponential decay occurs when the base $b$ is between 0 and 1. Here $0<0.76<1$.
c. Substitute $x=3$ into the given equation and compute the value.

Answer:

d. $600(1.04)^3$

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