1.19: Exponential function and small changes

0606/11/O/N/18 — Question 9 · 8 marks

Variables ss and tt are such that s=4t+3e−ts = 4t + 3\mathrm{e}^{-t}.
(i)
Find the value of ss when t=0t = 0.
[1]
(ii)
Find the exact value of tt when dsdt=2\dfrac{\mathrm{d}s}{\mathrm{d}t} = 2.
[4]
(iii)
Find the approximate increase in ss when tt increases from ln⁡5\ln 5 to ln⁡5+h\ln 5 + h, where hh is small.
[3]