helpme me please

Question

1. Find the rate of change of f (x)= x^+25 from x=-2 to x=1

 

2. Use long division to find the quotient and reminder: 6x^3 -x^2-5x+4/3x-2

 

3.  the exponential function passing through (0,3) and (2,12).

 

4. If $20,000 is invested at 2.5% per year compounded quarterly, find the value of the investment after 10 years.

 

5. Solve for x: 50 (1.02)^3x=200

 

6. Solve for y: log(5y-2)=1

 

Answer 1

1 x^2+25, rate of change from x=-2 to x=1

It's an upward opening parabola with vertex (0, 25)

from x=-2 to 1 is from points (-2,29) to (1,26)

the slope of the line through the two points = the rate of change

slope = change in y over change in x = (29-26)/(-2-1) = 3/-3 =-1

2 6x^3-x^2-5x+4 divided by 3x+2 = 2x^3 -5x^2/3 -5/9 with remainder of 46/9

3 y=3(2)^x or y= 3(-2)^x

goes through (0,3) and (2,12)

3=3(2)^0 = 3(1) =3

12=3(2)^2 =3(4) = 12

4 $20,000 invested at 2.5% for 10 years compounded quarterly

general formula is

A=P(1+r/n)^nt

P=20000

r=.025

n=4

t=10

A=20000(1+0.025/4)^4(10)

= 20000(1.00625)^40

=$25,660.54 rounded off to nearest cent = amount after 10 years at 2.5% compounded quarterly

5 50(1.02)^3x = 200

(1.02)^3x =200/50 =4

let y=3x

1.02^y = 4

y=70

3x =70

x=70/3 = about 23.3

6 log(5y-2)=1

10^1 = 5y-2

5y-2 =10

5y =12

y=12/5

y= 2.4