Given equations are
\(\displaystyle{y}_{{1}}={C}{e}^{{{k}_{{1}}{t}}}\)

\(\displaystyle{y}_{{2}}={C}{\left({2}^{{{k}_{{2}}{t}}}\right)}\)

They pass through points (0, 16) and \(\displaystyle{\left({60},{\frac{{{1}}}{{{4}}}}\right)}\)

now \(\displaystyle{y}_{{1}}={C}{e}^{{{k}_{{1}}{t}}},{\left({0},{16}\right)}\)

\(\displaystyle{16}={C}{e}^{{0}}={C}\)

\(\displaystyle{C}={16}\)

\(\displaystyle{y}_{{1}}={16}{e}^{{{k}_{{1}}{t}}},{\left({60},{\frac{{{1}}}{{{4}}}}\right)}\)

\(\displaystyle{\frac{{{1}}}{{{4}}}}={16}{e}^{{{60}{k}_{{1}}}}\)

\(\displaystyle{e}^{{{60}{k}_{{1}}}}={\frac{{{1}}}{{{64}}}}\)

\(\displaystyle{60}{k}_{{1}}={\ln{{\frac{{{1}}}{{{64}}}}}}=-{4.158883}\)

\(\displaystyle{k}_{{1}}={\frac{{-{4.158883}}}{{{60}}}}=-{0.0693}\)

\(\displaystyle{k}_{{1}}=-{0.0693}\)

Again

\(\displaystyle{y}_{{1}}={C}{2}^{{{k}_{{2}}{t}}},\)

\(\displaystyle{16}={C}{2}^{{0}}={C}\)

\(\displaystyle{C}={16}\)

\(\displaystyle{y}_{{1}}={16}\times{2}^{{{k}_{{2}}{t}}}\)

\(\displaystyle{\frac{{{1}}}{{{4}}}}={16}\times{2}^{{{60}{k}_{{2}}}}\)

\(\displaystyle{2}^{{{60}{k}_{{2}}}}={\frac{{{1}}}{{{64}}}}={2}^{{-{6}}}\)

\(\displaystyle{60}{k}_{{2}}=-{6}\)

\(\displaystyle{k}_{{2}}=-{\frac{{{6}}}{{{60}}}}=-{0.1}\)

\(\displaystyle{k}_{{2}}=-{0.1}\)

\(\displaystyle{C}={16}\)

\(\displaystyle{k}_{{1}}=-{0.0693}\)

\(\displaystyle{k}_{{2}}=-{0.1}\)

\(\displaystyle{y}_{{2}}={C}{\left({2}^{{{k}_{{2}}{t}}}\right)}\)

They pass through points (0, 16) and \(\displaystyle{\left({60},{\frac{{{1}}}{{{4}}}}\right)}\)

now \(\displaystyle{y}_{{1}}={C}{e}^{{{k}_{{1}}{t}}},{\left({0},{16}\right)}\)

\(\displaystyle{16}={C}{e}^{{0}}={C}\)

\(\displaystyle{C}={16}\)

\(\displaystyle{y}_{{1}}={16}{e}^{{{k}_{{1}}{t}}},{\left({60},{\frac{{{1}}}{{{4}}}}\right)}\)

\(\displaystyle{\frac{{{1}}}{{{4}}}}={16}{e}^{{{60}{k}_{{1}}}}\)

\(\displaystyle{e}^{{{60}{k}_{{1}}}}={\frac{{{1}}}{{{64}}}}\)

\(\displaystyle{60}{k}_{{1}}={\ln{{\frac{{{1}}}{{{64}}}}}}=-{4.158883}\)

\(\displaystyle{k}_{{1}}={\frac{{-{4.158883}}}{{{60}}}}=-{0.0693}\)

\(\displaystyle{k}_{{1}}=-{0.0693}\)

Again

\(\displaystyle{y}_{{1}}={C}{2}^{{{k}_{{2}}{t}}},\)

\(\displaystyle{16}={C}{2}^{{0}}={C}\)

\(\displaystyle{C}={16}\)

\(\displaystyle{y}_{{1}}={16}\times{2}^{{{k}_{{2}}{t}}}\)

\(\displaystyle{\frac{{{1}}}{{{4}}}}={16}\times{2}^{{{60}{k}_{{2}}}}\)

\(\displaystyle{2}^{{{60}{k}_{{2}}}}={\frac{{{1}}}{{{64}}}}={2}^{{-{6}}}\)

\(\displaystyle{60}{k}_{{2}}=-{6}\)

\(\displaystyle{k}_{{2}}=-{\frac{{{6}}}{{{60}}}}=-{0.1}\)

\(\displaystyle{k}_{{2}}=-{0.1}\)

\(\displaystyle{C}={16}\)

\(\displaystyle{k}_{{1}}=-{0.0693}\)

\(\displaystyle{k}_{{2}}=-{0.1}\)