1.6 Exponentials and logarithms

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Question 49

The variables $x$ and $y$ are connected by the relationship

\frac{10^{-15}}{x^{2.5}}, \quad x > 0

Sketch the graph of $log_{10} y$ against $log_{10} x$ . Clearly label the coordinates of the points of intersection of the graph with the coordinate axes.

[4]

ii.

A population of microbes $N$ increases over time $t$ hours according to the model $N = ab^t$ , where $a$ and $b$ are positive constants. A scientist plots the linear relationship between $log_{9} N$ and $t$ . The resulting line has a positive gradient and passes through the points $(0, 2.5)$ and $(- 10, 0)$ . Determine the exact values of $a$ and $b$ .

[5]

The variables $x$ and $y$ are connected by the relationship

\frac{10^{-15}}{x^{2.5}}, \quad x > 0

Sketch the graph of $log_{10} y$ against $log_{10} x$ . Clearly label the coordinates of the points of intersection of the graph with the coordinate axes.

[4]

1.6 Exponentials and logarithms

Question 49

Markscheme

1.6 Exponentials and logarithms

Question 49

Markscheme

1.6 Exponentials and logarithms

Question 49

1.6 Exponentials and logarithms Questions

1.6 Exponentials and logarithms

Question 49

1.6 Exponentials and logarithms Questions