A conservation group pledges to plant trees by adopting areas throughout a region starting in 2020. The function A(t)=10+5t models the number of areas A the group will adopt t
years after 2020. The group also pledges that the number of trees in each area P models the function P(t)=25+4t , where t is the number of years after 2020. Explain whether the number of trees that are planted by the group in the year 2030 is 23,200 .
A) The number of trees planted by the group is 23,200 because the value of t is 30 in 2030. Multiplying A(30) by P(30) results in 23,200.
B) The number of trees planted by the group is not 23,200 because the value of t
is 1 in 2030. Multiplying A(1) by P(1) results in 435
C) The number of trees planted by the group is not 23,200 because the value of t is 10 in 2030. Adding A(10) by P(10) results in 125
D) The number of trees planted by the group is not 23,200 because the value of t is 10 in 2030. Multiplying A(10) by P(10) results in 3,900.
D) The number of trees planted by the group is not 23,200 because the value of t is 10 in 2030. Multiplying A(10) by P(10) results in 3,900.
is that correct?
No, D) is not the correct option. The correct option is A) The number of trees planted by the group is 23,200 because the value of t is 30 in 2030. Multiplying A(30) by P(30) results in 23,200.
D) The number of trees planted by the group is not 23,200 because the value of t is 10 in 2030. Multiplying A(10) by P(10) results in 3,900.
D) The number of trees planted by the group is not 23,200 because the value of t is 10 in 2030. Multiplying A(10) by P(10) results in 3,900.
To explain how we arrived at this answer, we need to substitute the value of t as 10, since we are looking for the number of trees planted in the year 2030.
The function A(t) represents the number of areas adopted by the group, with A(t) = 10 + 5t.
Substituting t as 10, we get A(10) = 10 + 5(10) = 10 + 50 = 60. So, the conservation group has adopted 60 areas in the year 2030.
The function P(t) represents the number of trees in each area, with P(t) = 25 + 4t.
Substituting t as 10, we get P(10) = 25 + 4(10) = 25 + 40 = 65. So, there are 65 trees in each adopted area in the year 2030.
To find the total number of trees planted, we multiply the number of areas adopted by the number of trees in each area.
Multiplying A(10) by P(10) gives us 60 * 65 = 3,900. Therefore, the number of trees planted by the group in the year 2030 is not 23,200, but rather 3,900.