contestada

The population of a city is growing according to the exponential model p = cekt, where p is the population in thousands and t is measured in years. if the population doubles every 11 years what is k, the city's growth rate? [round answer to the nearest hundredth.]
a.2.8%
b.4.4%
c.6.3%
d.8.9%

Respuesta :

budwilkins
p = ce^(kt)
make p = 2c because doubling will be
like c-->2c, so if p = 2c, then
p = ce^(kt)
2c = ce^(kt)
2c/c = (ce^(kt))/c
2 = e^(kt)
Now take natural logarithm (ln) of both sides of the equation:
ln (2) = ln (e^(kt))
0.693 = kt×ln e
**this is because ln of an exponent makes the exponent become multiplied by the ln,
and ln e = 1
0.693 = kt×ln e
0.693 = kt×1, and t = 11 years
0.693 = k(11)
0.693/11 = 11k/11
k = 0.063, multiply by 100 to get %
k = 6.3%
answer is C

The value of k is 6.3% if the population of a city is growing according to the exponential model p = cekt, where p is the population in thousands and t is measured in years option (C) is correct.

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 [tex]\rm y = a^x[/tex]

where 'a' is a constant and a>1

We have an exponential model:

[tex]\rm p = ce^{kt}[/tex]

When t = 11 years, P = 2C

[tex]\rm 2C = Ce^{11k}[/tex]

[tex]\rm 2 = e^{11k}[/tex]

After taking ln

ln2 = 11k

k = 0.063

k = 6.3%

Thus, the value of k is 6.3% if the population of a city is growing according to the exponential model p = cekt, where p is the population in thousands and t is measured in years.

Learn more about the exponential function here:

brainly.com/question/11487261

#SPJ2

Otras preguntas