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Luden [163]
3 years ago
10

At a local high school, the student population is growing at 12% a year. If the original population was 242 students, how long w

ill it take the population to reach 300 students? Round to the nearest tenth of a year.
Mathematics
1 answer:
uranmaximum [27]3 years ago
8 0

Answer: 2 years

Step-by-step explanation:

The exponential growth function is given by :-

y=A(1+r)^x (i)

, where A = initial value , r = rate of growth and  x= time period.

As per given ,

A= 242

r= 12% = 0.12

To find : t when y= 300.

Put all the values in (i)

300=242(1+0.12)^x\\\\\Rightarrow\ \dfrac{300}{242}=(1.12)^x\\\\\Rightarrow\ 1.23967=(1.12)^x

Taking log on both sides , we get

\log (1.2396) = t \log (1.12)\\\\\Rightarrow\ 0.09328=t(0.049218)\\\\\Rightarrow t=\dfrac{0.09328}{0.049218}=\approx2

hence, it will take 2 years.

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