sat suite question viewer

Advanced Math / Nonlinear functions Difficulty: Medium

$f left parenthesis x right parenthesis equals 3,000 left parenthesis 0.75 right parenthesis Superscript x$

A conservation scientist implemented a program to reduce the population of a certain species in an area. The given function estimates this species' population $x$ years after $2008$ , where $x less than or equals 8$ . Which of the following is the best interpretation of $3,000$ in this context?

The estimated percent decrease in the population for this species and area every $8$ years after $2008$

The estimated percent decrease in the population for this species and area each year after $2008$

The estimated population for this species and area $8$ years after $2008$

The estimated initial population for this species and area in $2008$

Back question 190 of 229 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229

Explanation

Choice D is correct. Substituting $0$ for $x$ in the given equation yields $f left parenthesis 0 right parenthesis equals 3,000 left parenthesis 0.75 right parenthesis Superscript 0$ , which is equivalent to $f left parenthesis 0 right parenthesis equals 3,000 left parenthesis 1 right parenthesis$ , or $f left parenthesis 0 right parenthesis equals 3,000$ . It’s given that the function estimates the species’ population $x$ years after $2008$ , so it follows that the estimated population of the species is $3,000$ in $2008$ . Therefore, the best interpretation of $3,000$ in this context is the estimated initial population for this species and area in $2008$ .

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect. The estimated percent decrease in the population for this species and area each year after $2008$ is $25 percent sign$ , not $3,000$ .

Choice C is incorrect. The estimated population for this species and area $8$ years after $2008$ is $3,000 left parenthesis 0.75 right parenthesis Superscript 8$ , or approximately $300$ , not $3,000$ .