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AQA A Level - Exponential & Log Basics

Exponential Functions, Logs & Log Laws

AQA 7356/1 Jun 2022 AS Exam Q. 1 :   1 mark in 1:08 min.
AQA 7357/2 Jun 2022 A2 Exam Q. 9 :   4 marks in 4:48 min.
AQA 7356/2 Nov 2021 AS Exam Q. 6 :   3 marks in 3:22 min.
AQA 7357/2 Nov 2021 A2 Exam Q. 6 :   4 marks in 4:48 min.
AQA 7356/2 Nov 2020 AS Exam Q. 8 :   6 marks in 6:45 min.
AQA 7357/1 Jun 2019 A2 Exam Q. 1 :   1 mark in 1:12 min.
AQA 7357/2 Jun 2019 A2 Exam Q. 2 :   1 mark in 1:12 min.
AQA 7356/2 Jun 2019 AS Exam Q. 4 :   4 marks in 4:30 min.
AQA 7356/2 Jun 2018 AS Exam Q. 3 :   2 marks in 2:15 min.
AQA 7357/3 Jun 2018 A2 Exam Q. 7 :   5 marks in 6:00 min.
AQA 7356/2 Jun 2017 AS Sample Exam Q. 3 :   2 marks in 2:15 min.
Using exponential functions
Using logarithms to any base
Explore relationship between exponential functions and their derivatives
Exponential Graphs: ${a^x}$
The graph of $\color{blue}{ f(x) = {a^x} }$ is shown in blue, together with its tangent and gradient at a sample point in red.

By considering the gradient at x = 0, 1, 2, 3, can you predict what the gradient function of $\color{blue}{ f(x) = {a^x} }$ is?
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Gradients of ${a^x}$ and ${e^x}$
Compare the graph of \(\color{blue}{ f(x) = {a^x} }\) with the graph of its gradient function, \(\color{green}{ f'(x) }\).
Adjust the value of a till the the two curves coincide.
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