Question

nameperioddatetopic 06 – class 04 – exponential growth and decayself-assessment 1 i dont understand yet 2 i can do it with help 3 i can do it on my own 4 i can help someone else1. a website has 500,000 members in 2020. the number y of members increases by 15% each year.a. write a function that represents the website membership t years after 2020.b. about how many members will there be in 2026?when does the function $y = ab^x$ represent exponential growth?ssment 1 i dont understand yet 2 i can do it with help. 3 i can do itwhether the table represents an exponential grtion, or neither. explain.

Explanation:

Step1: Define growth function form

The standard exponential growth function is $y = a(1+r)^t$, where $a$ is the initial amount, $r$ is the growth rate, and $t$ is time in years.

Step2: Plug in values for part a

Here, $a=500000$, $r=0.15$. Substitute to get:
$y = 500000(1+0.15)^t = 500000(1.15)^t$

Step3: Find t for 2026 for part b

2026 is $2026-2020=6$ years after 2020, so $t=6$.

Step4: Calculate membership for 2026

Substitute $t=6$ into the function:
$y = 500000(1.15)^6$
First calculate $(1.15)^6 \approx 2.313060765625$
Then $y \approx 500000 \times 2.313060765625 = 1156530.3828125$

Step5: State growth condition for $y=ab^x$

For exponential growth, the base $b$ must be greater than 1, and $a>0$.

Answer:

a. $y = 500000(1.15)^t$
b. About 1,156,530 members
The function $y=ab^x$ represents exponential growth when $a>0$ and $b>1$.