10 Layla invests money in the bank and receives compound interest. The amount \(\pounds L\) that she has after \(t\) years is given by the equation \(\mathrm { L } = 2800 \times 1.023 ^ { \mathrm { t } }\).
- State the amount she invests.
- State the annual rate of interest.
Amit invests \(\pounds 3000\) and receives \(2 \%\) compound interest per year. The amount \(\pounds A\) that he has after \(t\) years is given by the equation \(\mathrm { A } = \mathrm { ab } ^ { \mathrm { t } }\).
- Determine the values of the constants \(a\) and \(b\).
- Layla and Amit invest their money in the bank at the same time.
Determine the value of \(t\) for which Layla and Amit have equal amounts in the bank. Give your answer correct to \(\mathbf { 1 }\) decimal place.