the population of collin county, which follows the exponential growth model, increased from 491,675 in 2000 to 782,341 in 2010.

Question

1 year ago

10

a. find the exponential growth rate, k. don’t round, instead use the exact value of the growth rate.

1 answer:

CaHeK987 [17] · Answer 1 · 2024-02-14T18:15:57+03:00

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

Read more about the exponential growth model here:

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