Respuesta :

semsee45

Answer:

[tex]P=236000(1+0.04)^t[/tex]

Step-by-step explanation:

Exponential equation:  [tex]y=a(1+r)^x[/tex]

where:

  • [tex]a[/tex] is the initial value
  • [tex]r[/tex] is the growth rate (in decimal form)
  • [tex]x[/tex] is the independent variable
  • [tex]y[/tex] is the dependent variable

Given:

  • Population is increasing at a rate of 4% each year
  • Population in 2000 was 236000
  • Let t = number of years since 2000
  • Let P = population

Therefore,

  • [tex]a[/tex] = 236000
  • [tex]r[/tex] = 4% = 4/100 = 0.04
  • [tex]t[/tex] is the independent variable
  • [tex]P[/tex] is the dependent variable

[tex]\implies P=236000(1+0.04)^t[/tex]

Note the rule

[tex]\\ \rm\rightarrowtail y=P(1+\dfrac{r}{100})^t[/tex]

Now

  • P=236000
  • Rate of change=r=4%

Put it

[tex]\\ \rm\rightarrowtail y=236000(1+4/100)^t[/tex]

[tex]\\ \rm\rightarrowtail y=236000(1+0.04)^t[/tex]

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