WHAT IS 543,821 ROUND TO THE NEARST THOUSAND
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Katie wants to collect over 100 seashells. She already has 34 seashells in her collection. Each day, she finds 12 more seashells on the beach. Katie can use fractions of days to find seashells.
Write an inequality to determine the number of days, d, it will take Katie to collect over 100 seashells
<em><u>Answer:</u></em>
Kathie needs more than 5 days to get over 100 shells
The required inequality is
<em><u>Solution:</u></em>
Given that,
Katie wants to collect over 100 seashells.
She already has 34 seashells in her collection.
Each day, she finds 12 more seashells on the beach
Let "d" be the number of days she takes to cover 100 sea shells
From given statement,
She finds 12 seashells each day
Then for "d" days, the number of sea shells she collected is 12d
She already had = 34
So, the equation can be framed as:
Here we used "greater than" symbol, since she wants to collect over 100 seashells
Solve the inequality
This means she won't have more than 100 shells until the 6th day
Thus she needs more than 5 days to get over 100 shells
Answer:
Part A)
Chorus:
Band:
Part B)
After 9 years:
The chorus will have about 41 people.
And the band will have 48 people.
Part C)
About approximately 11 years.
Step-by-step explanation:
We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.
There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.
Part A)
Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.
So, using the standard form for exponential growth:
Where <em>a</em> is the initial population and <em>r</em> is the rate of change.
We will substitute 15 for <em>a </em>and 1.12 for <em>r</em>. Hence:
This represents the number of people in the chorus after <em>t</em> years.
We are given that 2 new people join the band each year. So, it increases linearly.
Since there are already 30 people in the band, our initial point or y-intercept is 30.
And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:
And by substitution:
This represents the number of people in the band after <em>t</em> years.
Part B)
We want to find the number of people in the chorus and the band after 9 years.
Using the chorus function, we see that:
There will be approximately 41 people in the chorus after 9 years.
And using the band function, we see that:
There will be 48 people in the band after 9 years.
Part C)
We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for <em>t</em>. So:
Unfortunately, it is impossible to solve for <em>t</em> using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.
Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).
Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.
