Question

the population of collin county, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010. a. find the exponential growth rate, k. don’t round, instead use the exact value of the growth rate.

Answer 1

Applying the formula for the exponential growth model, the growth rate is  0.046447277776453351798354258063923

the exponential growth is a data pattern that illustrates an increase over time by generating an exponential function curve.

The exponential growth model can be expressed as:

P(t) = P(0) x e^(k.t)

Where:

P(t) = Value at time t

P(0) = Initial value

k = growth rate

Information from the problem:

P(0) = 491,675

P(t) = 782,341

t = 2010 - 2000 = 10 years

Substitute the data into the formula:

782,341 = 491,675 x e^{10k}

e^{10k} = 782,341 / 491,675

10 k . ln e = ln (782,341 / 491,675)

10 k = 0.46447277776453351798354258063923

k = 0.046447277776453351798354258063923

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