Answer :
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:
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