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Dmitry_Shevchenko [17]
3 years ago
10

During the first decade of the century, the population of a certain city was 145,380 in 2000 and 219,135 in 2010. Find the expon

ential growth function that models the growth of the city. Use t = 0 to represent 2000, t = 10 to represent 2010, and so on ( round k to five decimal places)
Mathematics
1 answer:
Likurg_2 [28]3 years ago
8 0

Answer:

The exponential growth function is P=145380e^{0.04103t}

Step-by-step explanation:

Given: The population of a certain city was 145,380 in 2000 and 219,135 in 2010.

To find: exponential growth function that models the growth of the city

Solution:

The exponential growth function is given by P=P_0 e^{kt}

Here, P denotes total population after time t

P_0 denotes initial population

k denotes rate of growth

t denotes time

As P(0)=145,380,

145380=P_0e^{0}\\145380=P_0\\P=145380e^{kt}

As P(10)=219135

219135=145380e^{10k}\\e^{10k}=\frac{219135}{145380}\\=1.507326\\k=\frac{1}{10}\ln (1.507326)\\=0.04103\\\Rightarrow P=145380e^{0.04103t}

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