Problem 1 Problem 2 Problem 3 Driving at 60 mihr it takes ap

Problem #1

Problem #2

Problem #3

Driving at 60 mi/hr, it takes approximately 3.5 hours to drive from Long Island to Albany, NY.

Problem #4

1) f(x) =mx^1/2

g(x) = kx^3/2

blue graph passes through (1,2) : 2 = m(1)^1/2 ---> m = 2

they intersect at (4 , t): mx^1/2 = kx^3/2 ; x =2

m = kx ---> 2 = k(4) ---> k = 1/2

f(x) = 2x^1/2 ; plug (4,t)

t = 2(4)^1/2 ----> t = 2*2 =4

2) f(1) = 8 ; f(2) = 104

a) linear function: f(x) = ax +b

a +b =8

2a + b = 104

------------- (-1)

-a = -96 ---> a =96 ; b = 8-96 = -88

f(x) = 96x -88

b) power function:

f(x) = a(x)^b ; f(1) = 8 ; f(2) = 104

8 = a(1)^b ---> a = 8

104 = a2^b---> 2^b = 13

take log on both sides:

bln(2) = ln(13)

b = 3.7

So, f(x) =8x^3.7

c) exponential function:

f(x) = ab^x ; f(1) = 8 ; f(2) = 104

8 = ab^1 ---> ab = 8

104 = ab^2 ---> ab^2 = 104

ab^2/ab = 104/8 = 13

b = 13

a = 8/13

f(x) = (8/13)(13)^x