ALGEBRA PLEASE HELP ANSWER BOTH! I need the steps and the answers..

23.

a)The object hits 150 feets after 9 seconds or 1 second

b)150 ft , time is 9 sec or 1 sec

24.

a) y=125000(0.8)^x

b)$40960

Step-by-step explanation:

23.

Given the equation that models the height as

h=-16t²+160t+6 and h=150, re-write the equation as

150=-16t²+160t+6

150-6=-16t²+160t

144=-16t²+160t

16t²-160t+144=0divide the terms by 16

t²-10t+9=0

factorize as

t²-t-9t+9=0

t(t-1)-9(t-1)=0

(t-9)(t-1)=0

t-9=0

t=9  or

(t-1)=0

t-1=0

t=1

The object hits 150 feets after 9 seconds or 1 second

b) maximum height is given as

h=-16t²+160t+6

h=-16(9²)+160*9+6

h= -1296 + 1440+6 = 150 ft

Time taken is 9 seconds or 1 second

24.

a)The formula for exponential decay is ;

y=a(1-b)^x

where

a=original amount

b=decay factor as a percentage

x=exponent, how often the decay occurs

Given that;

a=$125000

b=20% =0.2

Then

y=125000(1-0.2)^x

y=125000(0.8)^x is the exponential decay function

b)Given x=5

y= 125000(0.8)^5 =$40960

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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