How do scientists perform an artificial transmutation?

they bombard nuclei with high-energy particles, such as protons, neutrons, or alpha particles.

they use a particle accelerator to speed up nuclear decay.

they use a strong electric current to remove neutrons from an atom.

They bombard nuclei with high-energy particles, such as protons, neutrons, or alpha particles.  

Explanation:

Scientist are performing artificial transmission by bombarding atomic nuclei with high energy particle such as neutron, proton and alpha particle. Nucleus decay is an example of transmutation which occurs naturally.  Elements with electronic number which is greater than 92 is called trans uranium element.  

All trans uranium elements are radioactive which is found is nature. Some transmutation requires particles that are moving at extremely high speed. Scientist have produced nearly 3000 different isotopes.  

what image you forgot to include it.

9.9 years

a = p(1 + rt) . . account balance after time t at rate r starting with principal p

3000 = 2500(1 + 0.0202t) . . filling in the given numbers

1.2 = 1 + 0.0202t . . divide by 2500

0.2 = 0.0202t . . . subtract 1

0.2/0.0202 = t ≈ 9.901

it will take about 9.9 years for the account balance to reach $3000.