Question

the number of branches on a large tree after the year 2000 is represented by the following table:time (years) branches0 162 234 336 488 6910 99which model for $b(t)$, the number of branches $t$ years after the year 2000, best fits the data?choose 1 answer:a $b(t) = 16 + 7 \cdot t$b $b(t) = 16 \cdot (1.44)^t$c $b(t) = 16 \cdot (1.2)^t$d $b(t) = 16 + 30 \cdot t$

Explanation:

Step1: Test linear model A

For $t=2$: $B(2)=16+7\cdot2=30$ (actual=23, large error)
For $t=4$: $B(4)=16+7\cdot4=44$ (actual=33, large error)

Step2: Test exponential model B

For $t=2$: $B(2)=16\cdot(1.44)^2=16\cdot2.0736=33.1776$ (actual=23, large error)
For $t=4$: $B(4)=16\cdot(1.44)^4=16\cdot(2.0736)^2\approx68.87$ (actual=33, large error)

Step3: Test exponential model C

For $t=2$: $B(2)=16\cdot(1.2)^2=16\cdot1.44=23.04$ (actual=23, small error)
For $t=4$: $B(4)=16\cdot(1.2)^4=16\cdot2.0736=33.18$ (actual=33, small error)
For $t=6$: $B(6)=16\cdot(1.2)^6=16\cdot2.985984\approx47.78$ (actual=48, small error)
For $t=8$: $B(8)=16\cdot(1.2)^8=16\cdot4.29981696\approx68.797$ (actual=69, small error)
For $t=10$: $B(10)=16\cdot(1.2)^{10}=16\cdot6.191736422\approx99.068$ (actual=99, small error)

Step4: Test linear model D

For $t=2$: $B(2)=16+30\cdot2=76$ (actual=23, massive error)

Answer:

C. $B(t) = 16 \cdot (1.2)^t$