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A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week. Write an exponential growth function that represents the weight of the catfish after t weeks during the 8-week period.

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Respuesta :

carlosego
For this case we have an equation of the form:

 [tex] y = A * (b) ^ t [/tex] 
 Where,
 A: initial weight of the channel.
 b: growth rate
 t: time in weeks.
 Substituting values we have:
 [tex] y = 0.1 * (1.23) ^ t [/tex] 
 Where, the domain is:
 [0, 8]
 Answer:
 an exponential growth function that represents the weight of the catfish after t weeks during the 8-week period is:
 [tex] y = 0.1 * (1.23) ^ t [/tex] 
 Domain:
 [0, 8]
The equation is 
[tex]y=0.1(1.23)^t[/tex].

Explanation:
Exponential functions are given by y=a(1+r)ˣ, where a is the initial amount, r is the rate of growth, and x is the amount of time. In our case, a=0.1, r=0.23 and t=x.

This gives us
[tex]y=0.1(1+0.23)^t[/tex]
which simplifies to
[tex]y=0.1(1.23)^t[/tex].