Question

C) A low-projection scenario for the world population for 1995-2150 by the United Nations is given by the function y = -0.24r + 44.52x + 5481.63, where x is the number of years after 1990 and the world population is measured in millions of people. 1) Determine the input and output at the vertex of the graph of this model and interpret each value. Input value means Output value means 2) For what years after 1995 does this model predict that the population will increase? 3) For what years will the population exceed 6 billion? D) A farmer's main cash crop is tomatoes and the tomato harvest begins in the month of May. The number of bushels of tomatoes harvested on the xth day of May is given by the equation B(x) = 4(x + 1). How many bushels did the farmer harvest on May 15?

Answer 1

c)1.

Year	x	y
1995	5	5698.23
1996	6	5740.11
1997	7	5781.51
1998	8	5822.43
1999	9	5862.87
2000	10	5902.83
2001	11	5942.31
2002	12	5981.31
2003	13	6019.83
2004	14	6057.87
2005	15	6095.43
2006	16	6132.51
2007	17	6169.11
2008	18	6205.23
2009	19	6240.87
2010	20	6276.03
2011	21	6310.71
2012	22	6344.91
2013	23	6378.63
2014	24	6411.87
2015	25	6444.63
2016	26	6476.91
2017	27	6508.71
2018	28	6540.03
2019	29	6570.87
2020	30	6601.23
2021	31	6631.11
2022	32	6660.51
2023	33	6689.43
2024	34	6717.87
2025	35	6745.83
2026	36	6773.31
2027	37	6800.31
2028	38	6826.83
2029	39	6852.87
2030	40	6878.43
2031	41	6903.51
2032	42	6928.11
2033	43	6952.23
2034	44	6975.87
2035	45	6999.03
2036	46	7021.71
2037	47	7043.91
2038	48	7065.63
2039	49	7086.87
2040	50	7107.63
2041	51	7127.91
2042	52	7147.71
2043	53	7167.03
2044	54	7185.87
2045	55	7204.23
2046	56	7222.11
2047	57	7239.51
2048	58	7256.43
2049	59	7272.87
2050	60	7288.83
2051	61	7304.31
2052	62	7319.31
2053	63	7333.83
2054	64	7347.87
2055	65	7361.43
2056	66	7374.51
2057	67	7387.11
2058	68	7399.23
2059	69	7410.87
2060	70	7422.03
2061	71	7432.71
2062	72	7442.91
2063	73	7452.63
2064	74	7461.87
2065	75	7470.63
2066	76	7478.91
2067	77	7486.71
2068	78	7494.03
2069	79	7500.87
2070	80	7507.23
2071	81	7513.11
2072	82	7518.51
2073	83	7523.43
2074	84	7527.87
2075	85	7531.83
2076	86	7535.31
2077	87	7538.31
2078	88	7540.83
2079	89	7542.87
2080	90	7544.43
2081	91	7545.51
2082	92	7546.11
2083	93	7546.23
2084	94	7545.87
2085	95	7545.03
2086	96	7543.71
2087	97	7541.91
2088	98	7539.63
2089	99	7536.87
2090	100	7533.63
2091	101	7529.91
2092	102	7525.71
2093	103	7521.03
2094	104	7515.87
2095	105	7510.23
2096	106	7504.11
2097	107	7497.51
2098	108	7490.43
2099	109	7482.87
2100	110	7474.83
2101	111	7466.31
2102	112	7457.31
2103	113	7447.83
2104	114	7437.87
2105	115	7427.43
2106	116	7416.51
2107	117	7405.11
2108	118	7393.23
2109	119	7380.87
2110	120	7368.03
2111	121	7354.71
2112	122	7340.91
2113	123	7326.63
2114	124	7311.87
2115	125	7296.63
2116	126	7280.91
2117	127	7264.71
2118	128	7248.03
2119	129	7230.87
2120	130	7213.23
2121	131	7195.11
2122	132	7176.51
2123	133	7157.43
2124	134	7137.87
2125	135	7117.83
2126	136	7097.31
2127	137	7076.31
2128	138	7054.83
2129	139	7032.87
2130	140	7010.43
2131	141	6987.51
2132	142	6964.11
2133	143	6940.23
2134	144	6915.87
2135	145	6891.03
2136	146	6865.71
2137	147	6839.91
2138	148	6813.63
2139	149	6786.87
2140	150	6759.63
2141	151	6731.91
2142	152	6703.71
2143	153	6675.03
2144	154	6645.87
2145	155	6616.23
2146	156	6586.11
2147	157	6555.51
2148	158	6524.43
2149	159	6492.87
2150	160	6460.83

2. It is evident from the calculation that for 88 years , population will increase. After that it tends to decrease.

3. For 147 years, after 2003, the population will be more than 6 billion.

D) The equation is given by

B(C) = 4(2+1)

Putting x=15 in the equation,

we get B(15)=161.2698944$\simeq$161

Hence he harvested 161 bushels on May 15.