Respuesta :

ismaelconeme

Answer:

2.60 gr

Step-by-step explanation:

We need to consider the function [tex]P(t) = P_oe^{kt}[/tex] where Po is the initial substance k is the rate of decay and t is the time

We know that [tex]P_o = 14[/tex] and at the 7 th year P(t) is 7

This means

[tex]7 = 14e^{7k}[/tex]

We solve for k

[tex]\frac{7}{14} = e^{7k}\\\\\ln (\frac{7}{14}) = 7k\\\\k = \frac{\ln (7/14)}{7} = -0.099\\\\Then \ P(t) = 14e^{-0.099t}\\\\Now \  we \ take \ t = 17\\\\P(17) = 14e^{(-0.099)(17)} = 2.60[/tex]

fichoh

Using the exponential formular, the amount of the substance left after 17 years would be 2.60 grams.

Using the exponential function :

  • [tex]P(t) = P_{0}e^{kt} [/tex]
  • P0 = initial value ; t = time ; k = rate

Substituting the values into the expression

P(t) = P(7) = 7

[tex]7 = 14 e^{7k} [/tex]

[tex]\frac{7}{14} = e^{7k} [/tex]

[tex] 0.5= e^{7k} [/tex]

Take the In

[tex] -0.693147 = 7k [/tex]

k = - 0.099

Now we have the expression as : [tex]P(t) = P_{0}e^{-0.099t} [/tex]

After 17 years :

[tex]P(17) = 14e^{-0.099(17)} = 2.60 [/tex]

Hence, the amount of the substance left after 17 years is 2.60 grams.

Learn more : https://brainly.com/question/24423994

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