contestada

A little-known species of insect is approaching extinction, with a population that falls by 10%
every year. There are currently 2,400 insects remaining. How many will there be in 4 years?

Respuesta :

  • Rate of fall=10%=0.1
  • Current=2490
  • Time=4yr

The equation is

  • y=ab^x
  • y=(2400)(1-0.1)^4
  • y=2400(0.9)⁴
  • y=1574.6

Approximately 1575

semsee45

Answer:

approximately 1,575 insects

Step-by-step explanation:

We can model this as an exponential equation.

General form of an exponential equation:  [tex]y=ab^x[/tex]

where:

  • a is the initial value)
  • b is the base (or growth/decay factor)
  • x is the independent variable
  • y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

If the population falls by 10% each year, then each year the population will be 90% of the previous year (since 100% - 10% = 90%)

Convert 90% into a decimal:  90/100 = 0.9

Therefore, the base of the exponential function is 0.9

Given:

  • a = 2400
  • b = 0.9
  • x = time (in years)
  • y = population of insects

[tex]\implies y=2400(0.9)^x[/tex]

To find how many insects there will be in 4 years, substitute x = 4 into the equation and solve for y:

[tex]\begin{aligned}x=4 \implies y & =2400(0.9)^4\\& = 1574.64\end{aligned}[/tex]

Therefore, there will be approximately 1,575 insects remaining in 4 years.

Otras preguntas