f(x)=ekx+2−5f(x)=e^{kx+2}-5f(x)=ekx+2−5, where k k\,k is a positive constant.
State the range of fff
The curve y=f(x)y=f(x)y=f(x) meets the yyy-axis at A A\,A and the xxx-axis at BBB. Given that B:(ln5−23,0)\displaystyle B:\left(\frac{\ln 5-2}{3},0\right)B:(3ln5−2,0), find the exact coordinates of A A\,A and the value of kkk.
Find the equation of the tangent to the curve at AAA.
277 exam-style questions on Edexcel A Level Maths Exponentials and Logarithms, covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data. Each one has a worked solution and a mark scheme showing where the marks go.