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1. Given that $f(x) = (\sqrt 5)^x$, what is the range of $f(x)$ on the interval $[0, \infty)$?

2. When Lauren was born on January 1, 1990, her grandparents put $\$1000$ in a savings account in her name. The account earned $7.5\%$ annual interest compounded quarterly every three months. To the nearest dollar, how much money was in her account when she turns two?

 

Can someone also explain compound interest 

Guest Apr 8, 2018
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2.

2. When Lauren was born on January 1, 1990, her grandparents put $\$1000$ in a savings account in her name. The account earned $7.5\%$ annual interest compounded quarterly every three months. To the nearest dollar, how much money was in her account when she turns two?

 

Can someone also explain compound interest 

 

To solve this problem, you would use this financial formula:

FV = PV x [1 + R]^N, Where R=Interest rate per period, N=number of periods, PV=Present value, FV=Future value.

FV = $1,000 x [1 + 0.75/4]^(2*4)

FV = $1,000 x [1 + 0.01875]^8

FV = $1,000 x [1.01875]^8

FV = $1,000 x     1.16022167......

FV = $1,160 - What Lauren will have in her account when she turns two.

 

Compound interest is interest earned on interest!!. Example: You invest $1,000 at 5% annual compound for 3 years, how much will you have at the end of 3 years:

$1,000 x 1.05 = $1,050 - This is how much you will have at the end of first year. Now, you will take this amount of $1,050 x 1.05 =$1,102.50 - and this is how much you will have at the end of the second year. You see that $2.50 is interest you earned on the $50 interest of the first year. Now, you take $1,102.50 x 1.05 = $1,157.63 - and this is how much you will have in your account at the end of three years. That $7.63 is interest you earned on the $50 interest that you earned in the first year. This is what compound interest means. If it were "simple interest", then you would just earn $50 x 3 =$150 + $1,000 =$1,150. That difference of $7.63 is extra interest on interest, or compound interest.

Guest Apr 8, 2018
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1. 

\(f(x) = (\sqrt 5)^x \)

What is the range of  f(x)  on \([0, \infty)\)

 

This function is continuous on the requested interval

At  x  =  0, f(x)  = 1

Since √5  > 1, this function  is constantly increasing  on [0, inf)

 

So....the range   is   [1, infinity )  on  [0, infinity )

 

 

cool cool cool

CPhill  Apr 9, 2018

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