*n*years.

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Some questions I really don't understand. Please help on as many as you can. Thank you.

1) Write an expression using exponents, and find the total area of a pair of squares given their side lengths

a) 6cm,7cm

b)4cm,9cm

2)The population of deer on Mount Washington is 2500. If the growth of the deer population is 1.5% each year. Determine the expression that can be used to calculate the deer population after
*n* years.

a)P= 2500(1.5)^{n }

b)P= 250091.015)^{n}

c)P= 2500(1.15)^{n}

d)P= 2500(0.015)^{n}

3)Express each number as a product of two powers

a) 100

b) 108

c) 72

d) 2500

That's all! Thank you so much! :)

Tutors, sign in to answer this question.

Answer (1): since the area has the units of (length)^{2}....the total area of the pair of squares whose side lengths are:

(a) (6cm)^{2} + (7cm)^{2} = 36cm^{2} + 49cm^{2}

(b) (4cm)^{2} + (9cm)^{2} = 16cm^{2} + 81cm^{2}

Answer (2):

At n=1 year: P = 2500(1 + 0.015)

n=2 years: P = 2500(1 + 0.015) + [2500(1+0.015)](0.015) = 2500[1+2(0.015)+ (0.015)^{2}]

This looks like 2500(x^{2}+2x+1) or 2500(x+1)^{2} where x=0.015

Expand the equation at n=3 and you'll find that P will have the form 2500(x+1)(x^{2}+2x+1) = 2500(x+1)^{3 }where x=0.015

So P(n) = 2500(1+0.015)^{n} = 2500(1.015)^{n }where n=#of years

Answer (3):

(a) 100 = 25 x 4 = (5^{2})(2^{2})

(b) 108 = 27 x 4 = (3^{3})(2^{2})

(c) 72 = 9 x 8 = (3^{2})(2^{3)}

(d) 2500 = 100 x 25 = (10^{2})(5^{2})

1. a): A=Area = (6 cm)^{2} + (7 cm)^{2} = (36 cm^{2}) + (49 cm^{2}) =
**85 cm**^{2}

1. b) A = Area = (4 cm)^{2} + (9 cm)^{2} = (16 cm^{2}) + (81 cm^{2}) =
**97 cm**^{2}

2. The answer is d) ρ = 2500(0.015)^{n}

3. a) 100 = (2)(50) = (2)(2)(25) = (2)(2)(5)(5) = **(2**^{2})(5^{2})

3. b) 108 = (2)(54) = (2)(2)(27) = (2)(2)(3)(9) = (2)(2)(3)(3)(3) = **
(2**^{2})(3^{3})

3. c) 72 = (2)(36) = (2)(2)(18) = (2)(2)(2)(9) = (2)(2)(2)(3)(3) =**(2**^{3})(3^{2})

3. d) 2500 = 2(1250) = (2)(2)(625) = (2)(2)(5)(125) =(2)(2)(5)(5)(25) = (2)(2)(5)(5)(5)(5)

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