MATEMATİK I - Deneme Sınavı - 3

0=(e^x - 3)(e^x - 2)

So the system has 2 roots:

e^x - 3=0 then e^x=3 so x=ln3

e^x - 2=0 then e^x=2 so x=ln2

Therefore solution set is (ln2, ln3)

Since the half life is 3000 years, we can write:

0.5Q(0)=Q(0)*e^3000k which means that:

0.5=e^3000k

ln0.5=lne^3000k

ln0.5=3000k

ln0.5/3000=k

Thus, after finding k we can calculate:

Q(t=5000)=100*e^{5000*ln0.5/3000}

=100*e^5*ln0.5/3

=100*e^-1.155=31.49

Since we know that population doubles in 4 hours, we can write:

2Q(0)=Q(0)e^4k

2=e^4k

ln2=4k, so k=ln2/4=0.1733

Then Q(t=10)=1000e^10k

=1000.e^1.733

=5657 (approximately)

0.8Q=Q.e^10k

ln0.8/10=k=-0.0223

So we can find the half life by:

0.5Q=Q.e-^0.0223t

ln0.5=-0.0223t, then t=31.06 years

4*4*4*4=4⁴=256

x=4

The correct answer is 1.

The correct answer is 2928,2 ₺.

The correct answer is 4.

The correct answer is 70,71 gr.

6*6*6*6=6⁴=1296

The correct answer is 4.

The correct answer is 3.

7*7*7*7=2401; so 7⁴=2401; 

2000<7⁴<2500

The correct answer is 4.

2⁷=128

The correct answer is 7.

The correct answer is 2.

. We get  and . Hence, we find the solution to be x=-1 and x=3. 

The definition of logarithmic function cannot be x = -1. The solution is x=3.