Answer:
![z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%280.9808%29%5Et)
![z(t) = (1.0196)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0196%29%5Et)
![z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%280.9808%29%5Et)
![z(t) = (1.03)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.03%29%5Et)
![z(t) = (1.0404)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0404%29%5Et)
![z(t) = (1.0001)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%281.0001%29%5Et)
Step-by-step explanation:
We are given the following in the question:
![x(t)=(1.04)^t\\y(t)t=(1.02)^t](https://tex.z-dn.net/?f=x%28t%29%3D%281.04%29%5Et%5C%5Cy%28t%29t%3D%281.02%29%5Et)
We have to find the growth rate z(t) in each of the following cases:
(a) z = xy
![z(t) = x(t)y(t)\\z(t) = (1.04)^t.(1.02)^t\\z(t) = (1.04\times 1.02)^t\\z(t) = (1.0608)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20x%28t%29y%28t%29%5C%5Cz%28t%29%20%3D%20%281.04%29%5Et.%281.02%29%5Et%5C%5Cz%28t%29%20%3D%20%281.04%5Ctimes%201.02%29%5Et%5C%5Cz%28t%29%20%3D%20%281.0608%29%5Et)
(b) z=x/y
![z(t) =\displaystyle\frac{x(t)}{y(t)}\\\\z(t) = \frac{(1.04)^t}{(1.02)^t} = \bigg(\frac{1.04}{1.02}\bigg)^t\\\\z(t) = (1.0196)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cdisplaystyle%5Cfrac%7Bx%28t%29%7D%7By%28t%29%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%5Cfrac%7B%281.04%29%5Et%7D%7B%281.02%29%5Et%7D%20%3D%20%5Cbigg%28%5Cfrac%7B1.04%7D%7B1.02%7D%5Cbigg%29%5Et%5C%5C%5C%5Cz%28t%29%20%3D%20%281.0196%29%5Et)
(c) z=y/x
![z(t) =\displaystyle\frac{y(t)}{x(t)}\\\\z(t) = \frac{(1.02)^t}{(1.04)^t} = \bigg(\frac{1.02}{1.04}\bigg)^t\\\\z(t) = (0.9808)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cdisplaystyle%5Cfrac%7By%28t%29%7D%7Bx%28t%29%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%5Cfrac%7B%281.02%29%5Et%7D%7B%281.04%29%5Et%7D%20%3D%20%5Cbigg%28%5Cfrac%7B1.02%7D%7B1.04%7D%5Cbigg%29%5Et%5C%5C%5C%5Cz%28t%29%20%3D%20%280.9808%29%5Et)
(d) z=x^(1/2) y^(1/2)
![z(t) = (x(t))^{\frac{1}{2}}(y(t))^{\frac{1}{2}}\\z(t) = ((1.04)^t)^\frac{1}{2} ((1.02)^t)^\frac{1}{2}\\z(t) = (1.0608)^{\frac{t}{2}}\\z(t) = (1.03)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%28x%28t%29%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%28y%28t%29%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5Et%29%5E%5Cfrac%7B1%7D%7B2%7D%20%28%281.02%29%5Et%29%5E%5Cfrac%7B1%7D%7B2%7D%5C%5Cz%28t%29%20%3D%20%281.0608%29%5E%7B%5Cfrac%7Bt%7D%7B2%7D%7D%5C%5Cz%28t%29%20%3D%20%281.03%29%5Et)
(e) z=(x/y)^2
![z(t) =\bigg(\displaystyle\frac{x(t)}{y(t)}\bigg)^2\\\\z(t) =\bigg( \frac{(1.04)^t}{(1.02)^t}\bigg)^2 = \bigg(\frac{1.04}{1.02}\bigg)^{2t}\\\\z(t) = (1.0404)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%5Cbigg%28%5Cdisplaystyle%5Cfrac%7Bx%28t%29%7D%7By%28t%29%7D%5Cbigg%29%5E2%5C%5C%5C%5Cz%28t%29%20%3D%5Cbigg%28%20%5Cfrac%7B%281.04%29%5Et%7D%7B%281.02%29%5Et%7D%5Cbigg%29%5E2%20%3D%20%5Cbigg%28%5Cfrac%7B1.04%7D%7B1.02%7D%5Cbigg%29%5E%7B2t%7D%5C%5C%5C%5Cz%28t%29%20%3D%20%281.0404%29%5Et)
(f) z=x^(-1/3)y^(2/3)
![z(t) = (x(t))^{\frac{-1}{3}}(y(t))^{\frac{2}{3}}\\z(t) = ((1.04)^t)^{\frac{-1}{3}}((1.02)^t)^{\frac{2}{3}}\\z(t) = ((1.04)^{\frac{-1}{3}})^t((1.02)^{\frac{2}{3}})^t\\z(t) = (1.04^{\frac{-1}{3}}\times 1.02^{\frac{2}{3}})^t\\z(t) = (1.0001)^t](https://tex.z-dn.net/?f=z%28t%29%20%3D%20%28x%28t%29%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%28y%28t%29%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5Et%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%28%281.02%29%5Et%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5C%5Cz%28t%29%20%3D%20%28%281.04%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%29%5Et%28%281.02%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5Et%5C%5Cz%28t%29%20%3D%20%281.04%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%5Ctimes%201.02%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%29%5Et%5C%5Cz%28t%29%20%3D%20%281.0001%29%5Et)
Answer:
Step-by-step explanation:
Io
Answer:
I think B
Step-by-step explanation:
because their age group is 20-25 more of a constant age group
compared to 20-30
17. you add all numbers together and divide them by however many numbers you had to add to get that number.
Answer:
a 10 yd 2ft 7 in
b 10 yd 1 ft 2 in
c 99 yd
d. 4840 sq yd 7 sq ft 119 sq in
Step-by-step explanation:
a. 2 ft. 5 in. +
9 yd. 3 ft. 2 in.
---------------------
9 yd 5ft 7 in
but 3 ft = 1yd
9 yd 5ft 7 in
+1yd - 3ft
---------------------------
10 yd 2ft 7 in
b. 4 yd. 8 in
+ 6 yd. 6 in.
----------------------
10 yd 14 in
but 12 in = 1ft
10 yd 14 in
+ 1ft - 12 in
---------------------
10 yd 1 ft 2 in
c. 29 yd. 2 ft. 11 in.
55 yd. 1 ft. 10 in.
+ 13 yd. 1 ft. 3 in.
--------------------------
97 yd 4 ft 24 in
12 in = 1ft
24 in = 2ft
97 yd 4 ft 24 in
+2ft - 24 in
--------------------------------
97 yd 6ft
3 ft = 1yd
6f = 2yd
97 yd 6ft
+2yd - 6ft
---------------------
99 yd
d. 4,839 sq. yd. 8 sq. ft. 139 sq. in.
+ 7 sq. ft. 124 sq. in.
--------------------------------------------------
4839 sq yd 15 sq ft 263 sq in
12*12 = 144 sq in = 1 sq ft
4839 sq yd 15 sq ft 263 sq in
+ 1 sq ft - 144 sq in
--------------------------------------------------
4839 sq yd 16 sq ft 119 sq in
3ft * 3 ft = 9 sq ft = 1 sq yd
4839 sq yd 16 sq ft 119 sq in
+1 sq yd - 9 sq ft
----------------------------------------------
4840 sq yd 7 sq ft 119 sq in