The population of Ashmore was 925 in 2000 and in 1028 in 2001. the linear model for ashmores population is p= 103t+925, where th

Question

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The population of Ashmore was 925 in 2000 and in 1028 in 2001. the linear model for ashmores population is p= 103t+925, where th

e is the years since 2000.
Find an exponential model, in the form pm a (b)^2, for ashmores population t-ywars after 2000. round b to the nearest thousandth.

How much greater is the population predicted by the exponential model than that predicted by the linear model for the year 2015?

Mathematics

2 answers:

tester [12.3K] · Answer 1 · 2026-02-28T17:21:52+03:00

Answer:

The exponential population is 2035 more than what the linear model predicts.

Step-by-step breakdown:

The exponential model for Ashmore's population post-2000 is expressed as population = $a.(b)^{2}$ or population = $a.(r)^{t}$

In this case, "a" refers to Ashmore's population in 2000, which is 925.

r = growth factor = 1028/925 = 1.1113

t = number of years

Now we calculate the population for the year 2015:

$=925.(1.1113)^{15}$

= 925 × 4.87 = 4505

Population assessed via linear model for 2015:

p = 103t + 925

p = 103×15 + 925

p = 2470

The difference between the exponential and linear models is:

= 4505 - 2470 = 2035

tester [12.3K] · Answer 2 · 2026-02-28T17:21:45+03:00

To find the populations, perform the following calculation:

1028 / 925 = 1.11135

Hence, the exponential equation will be 925*1.11135^t

Calculating for a duration of 15 years: 925 * 1.11135^15 = 4507

For the linear model: 103(15) +925 = 2470

The difference between the exponential and linear predictions is 4507 - 2470 = 2037.