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use this information to answer the following questions
the function a(x) = 210(1.12)x represents the number of ants in ant colony a x days after an experiment starts. the graph represents the number of ants in ant colony b during the same time period. (1st picture is colony b)

how many ants in colony a per day, remember colony a is the function (2nd picture)

during week 0, how many more ants are there in ant colony a than in ant colony b?

find the growth rate of ant colony a.

find the growth rate of ant colony b.

use 1-2 complete sentences to compare the growth rate of ant colony a with ant colony b.

when does the daily number of ants in ant colony b exceed the daily number of ants in ant colony a? explain your answer using 1-2 complete sentences.

i will give even more points to the people who are correct and fast,

Step-by-step explanation:

Notice that with the percent growth, each year the company is grows by 50% of the

current year’s total, so as the company grows larger, the number of stores added in a year

grows as well.

To try to simplify the calculations, notice that after 1 year the number of stores for

company B was:

100 + 0.50(100) or equivalently by factoring

100(1+ 0.50) = 150

We can think of this as “the new number of stores is the original 100% plus another

50%”.

After 2 years, the number of stores was:

150 + 0.50(150) or equivalently by factoring

150(1+ 0.50) now recall the 150 came from 100(1+0.50). Substituting that,

100(1 0.50)(1 0.50) 100(1 0.50) 225 2 + + = + =

After 3 years, the number of stores was:

225 + 0.50(225) or equivalently by factoring

225(1+ 0.50) now recall the 225 came from 2 100(1+ 0.50) . Substituting that,

100(1 0.50) (1 0.50) 100(1 0.50) 337.5 2 3 + + = + =

From this, we can generalize, noticing that to show a 50% increase, each year we

multiply by a factor of (1+0.50), so after n years, our equation would be n B(n) = 100(1+ 0.50)

In this equation, the 100 represented the initial quantity, and the 0.50 was the percent

growth rate. Generalizing further, we arrive at the general form of exponential functions.

Exponential Function

An exponential growth or decay function is a function that grows or shrinks at a

constant percent growth rate. The equation can be written in the form x f (x) = a(1+ r) or x f (x) = ab where b = 1+r

Where

a is the initial or starting value of the function

r is the percent growth or decay rate, written as a decimal

b is the growth factor or growth multiplier. Since powers of negative numbers behave

strangely, we limit b to positive values.

To see more clearly the difference between exponential and linear growth, compare the

two tables and graphs below, which illustrate the growth of company A and B described

above over a longer time frame if the growth patterns were to continueExample 2

A certificate of deposit (CD) is a type of savings account offered by banks, typically

offering a higher interest rate in return for a fixed length of time you will leave your

money invested. If a bank offers a 24 month CD with an annual interest rate of 1.2%

compounded monthly, how much will a $1000 investment grow to over those 24

months?

First, we must notice that the interest rate is an annual rate, but is compounded monthly,

meaning interest is calculated and added to the account monthly. To find the monthly

interest rate, we divide the annual rate of 1.2% by 12 since there are 12 months in a

this story was prepared by jim

mccullaugh in los angeles and

al stewart in new york.

new york the colossal success of "top gun" appears to have dramatically altered madison avenue's

perception of corporate sponsorship

of home video projects.

the paramount home video re- lease, featuring a 60- second diet

pepsi spot, was by no means the

first prerecorded video to carry an advertiser's plug, but it was the

first major theatrical release to do so. in the aftermath of the title's

success, paramount is widely ex- pected to ink a similar deal for

"crocodile dundee" or "star trek

iv" or both.

corporate america's new attraccds push british

recording sales

to 19% gain

london fueled by the compact

disk boom, the value of u.k. manu- facturer shipments of recordings

rose 19% in the 12 -month period ended march 1987, according to the

british phonographic industry.

total value of u.k. shipments for

the period was $755 million for all

configurations. (all value figures

are based on an exchange rate of

$1.68 to the pound sterling.)

cd sales totaled 10.7 million units

worth $121.3 million- compared

with 3.7 million units worth $39.5

million in the prior 12 months -and

accounted for two -thirds of the

overall gain in trade value. at present growth rates, says the bpi, cd

sales for calendar 1987 will reach 20

(continued on page 79)

step-by-step explanation: