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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! :)

### 2 Answers by Expert Tutors

Alex V. | College doesn't make you smart. College teaches you to be resourceful.College doesn't make you smart. College ...
4.8 4.8 (73 lesson ratings) (73)
2
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 = 36cm2 + 49cm2
(b) (4cm)2 + (9cm)2 = 16cm2 + 81cm2

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(x2+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)(x2+2x+1) = 2500(x+1)where x=0.015

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

(a) 100 = 25 x 4 = (52)(22)
(b) 108 = 27 x 4 = (33)(22)
(c) 72 = 9 x 8 = (32)(23)
(d) 2500 = 100 x 25 = (102)(52)
William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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1. a): A=Area = (6 cm)2 + (7 cm)2 = (36 cm2) + (49 cm2) = 85 cm2

1. b) A = Area =  (4 cm)2 + (9 cm)2 = (16 cm2) + (81 cm2) = 97 cm2

2. The answer is d) ρ = 2500(0.015)n

3. a) 100 = (2)(50) = (2)(2)(25) = (2)(2)(5)(5) = (22)(52)

3. b) 108 = (2)(54) = (2)(2)(27) = (2)(2)(3)(9) = (2)(2)(3)(3)(3) = (22)(33)

3. c) 72 = (2)(36) = (2)(2)(18) = (2)(2)(2)(9) = (2)(2)(2)(3)(3) =(23)(32)

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

∴2500 = (22)(54)