Question

In 1900 Kansas City had a population of 163,000In 2020 it has a population of 1,686,000Show me exponential growthHow many years after 1900Did it take for the population to double

Answer 1

The exponential growth is 1.95% and after 35.72 years the population will double.

What is an exponential function?

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent $\rm y = a^x$

where a is a constant and a>1

Let's suppose the exponential growth function is:

$\rm y = Ae^{rt}$

A = 163,000

y = 1,686,000

t = 2020 – 1900 = 120 years

Plug all the values in the function:

$\rm 1686000 = 163000e^{120r}$

$\rm e^{120r} = 10.343$

Taking ln both side and solving:

r = 0.0194

r = 1.946 ≈ 1.95%

$\rm 2A = Ae^{0.0194t}$  (the population to double)

After solving:

t = 35.72 years

Thus, the exponential growth is 1.95% and after 35.72 years the population will double.

Learn more about the exponential function here:

brainly.com/question/11487261

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