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The mass of an isotope decreases at a rate that is proportional to the mass at that time.
The mass of the isotope was 40 grams initially, and it was 10 grams after 16 days.
What was the mass of the isotope after 20 days?

Sagot :

Answer:

7 milligrams

Step-by-step explanation:

ashishdwivedilVT

The mass of the isotope after 20 days is approximately 7 grams.

Suppose the mass of the isotope decreases exponentially according to the function given below.

[tex]m(t)=40a^t[/tex]

What is an exponential function?

A function of the form [tex]ab^x[/tex] is called an exponential function where b≠1.

The mass of the isotope was 10 grams after 16 days.

So, [tex]10=40a^{16}[/tex]

[tex]\frac{1}{4} =a^{16}[/tex]

[tex]a=0.917[/tex]

So, [tex]m(t)=40(0.917)^t[/tex]......(1)

So, to calculate the mass of the isotope after 20 days put t=20 in (1)

[tex]m(20)=40*0.917^{20}[/tex]

[tex]m(20)=7.07[/tex]

So, the mass of the isotope after 20 days is approximately 7 grams.

Hence, the mass of the isotope after 20 days is approximately 7 grams.

To get more about exponential functions visit:

https://brainly.com/question/2456547

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