Question

Please show your work

1. Marco is thinking of two numbers. Adding 5 times the first number and 8 times the second number gives a total of -13. Also, adding 5 times the first number and 10 times the second number gives -15. What are the two numbers?

2. The area of town A close to the pacific Ocean is currently 1500. Because of the rising sea level, the town is getting exponentially smaller every year. After every year, the area of the town decreases by 7%. What is the exponential function that represents the situation?

Answer 1

Explanation:

1. Subtract "Adding 5 times the first number and 8 times the second number gives a total of -13"

from "Also, adding 5 times the first number and 10 times the second number gives -15"

10 -8 = 2 times the second number gives -15 - (-13) = -2

the second number = -1

Put that in "adding 5 times the first number and 10 times the second number gives -15":

5 times the first number + 10(-1) = -15

5 times the first number = -5

the first number = -1

2. Given area of town A is currently 1500 and after every year, the area of the town decreases by 7%.

After 1 year. new area = 1500 * (1-7%)

After 2 years, new new area = 1500 * (1-7%) * (1-7%)

1 - 7% = 1 - 0.07 = 0.93

So the exponential function that represents the situation is 1500 * 0.93^(number of years)

Answer 2

1. 1st number be x, 2nd number be y

Adding 5 times the first number and 8 times the second number gives a total of -13

so 5x+8y=-13

Adding 5 times the first number and 10 times the second number gives -15

so 5x+10y=-15

subtracting the above two eqns

(5x+8y)-(5x+10y) = -13-(-15)

-2y=2

y=-1

put back in first eqn 5x+8(-1)=-13

5x=-5

x=-1

2. area of town A = 1500

every year, the area of the town decreases by 7%

so after 1 year, A=1500*(1-7%)=1500*(0.93)

after x years, A=1500(0.93)^x