SOLUTION: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)=1.8208e^.3387x, where x = 0 corresponds to 1998. In what year did/will the

Question 1024456: The value of China's exports of automobiles and parts (in billions of dollars) is approximately f(x)=1.8208e^.3387x, where x = 0 corresponds to 1998.
In what year did/will the exports reach $5.5 billion?

Give your answer as the year, with at least one decimal place
2. Students in a fifth-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score was given by the model
f(t)=95−7log(t+1), 0≤t≤24 where t is the time in months. Round answers to at least 1 decimal point.
(a) What is the average score on the original exam?

(b) What was the average score after 6 months?

(c) What was the average score after 18 months?

Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
For the value of exports to reach 5.5 billion, we have:
5.5=1.8208 e^.3387x
3.02065=e^.3387x
ln 3.02065=ln e^.3387x=.3387x
.3387x=1.1054721272885505026483318585694
x=3.2638681053692072708837669281647 years after 1998, which equals 2001.2639.
a)The average score on the original exam was:
95-7log(t+1)=95-7log(0+1)=95-7log1=95-0=95
b)After 6 months:
f(6)=95-7log(6+1)=95-7log7=95-5.92=89.08
c)After 18 months:
f(18)=95-7log(18+1)=95-8.95=86.04
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