Mathematics, 26.09.2019 18:50, o10889084

Belinda wants to invest $1000. the table below shows the value of her investment under two different options for three different years: number of years 1 2 3 option 1 (amount in dollars) 1100 1200 1300 option 2 (amount in dollars) 1100 1210 1331 part a: what type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? explain your answer. (2 points) part b: write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points) part c: belinda wants to invest in an option that would to increase her investment value by the greatest amount in 20 years. will there be any significant difference in the value of belinda's investment after 20 years if she uses option 2 over option 1? explain your answer, and show the investment value after 20 years for each option. (4 points)

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Part A: Option 1 is exponential because it does not increase by a constant rate. Option 2 is linear because it increases by a constant rate.

Part B:

For option 1: a(b)^x

a=1000 and b=1100/1000=1.1

the function will be:f(n)=1000(1.1)^x

For option 2:

Since the price increases by $100 each year, its linear.

Here would be the function: f(n)=1000+100(n)

Part C: Invest for 20 years in option 1: Yes.

f(20)=1000(1.1)^20

=1.1^20=6.72750

=6.72750x1000

=6727.50

y=6727.50, which is the price of the investment in 20 years.

For option 2:

f(20)=1000+100(20)

=1000+2000

=3000, which is the price the of the investment in 20 years.

If she uses option 2 rather than option 1, she will loose $3727.5

answered: Ahhskii

In option one, the investment grows by a constant of 100 per year, so it can be modeled by a linear equation.

f1(n)=1000+100n

In option two, the investment increases by a common ratio of 1.1, or increases by 10%, each year, and can thus be modeled by an exponential equation.

f2(n)=1000(1.1^n)

The exponential function will grow much larger versus the linear function because the rate of change increases every year...after 20 years

f1(20)=1000+100(20)=$3000

f2(20)=1000(1.1^20)=$6727.50 (to nearest cent)

So the exponential function is over 242% more than the linear function over this time period.

answered: Guest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

answered: Guest

i think its a and d

step-by-step explanation:

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Belinda wants to invest $1000. the table below shows the value of her investment under two different...