The population of bacteria in an experimental setup triples every 6 years. If the initial population of bacteria is equal to 200, what would be its population after \(t\) years?

Which of the exponential functions below are identical?

\(A: 3^{6x−2}\)

\(B: \dfrac{3^{6x}}{9}\)

\(C: \dfrac{729^x}{3}\)

What is the y-intercept and the range of the exponential function below?

\(g(x)=2.5^{x+2}−10\)

If \(\log_{10}⁡A=5\) and \(\log_{10}⁡B=3\), then what is the value of

\(\log_{10}\sqrt{AB^3} \,\)?

If \(\log_4⁡(x^2+4)=1.5\), then what is the value of \(x\)?

The per-square-foot rate of houses in a metro city increases by 10% every 6 months. The per-square-foot rate is \$100 in January 2020. What is the cost of a house of area 450 sq. ft in June 2021?

You may use a calculator.

Which option represents the function for the graph below?

The table below shows the relationship between time \(t\) and an observed quantity \(y\).

t	0	1	2.2	3.5	4.6	5
y	5.9	12.9	45.1	166.6	495.4	744.0

An exponential regression model of the form \(y=ab^t\) is fit to the data. Using a calculator, what is the predicted value of y when t = 6?

A purely exponentially decaying graph is translated by \(4\) units horizontally to the right and \(2\) units vertically downwards.

Which graph represents the function after the transformation?

Find the value of \(\dfrac{\log_{10}\ ⁡0.001}{\log_{2}⁡\ 0.25}\).

Two functions, \(h(x)\) and \(f(x)\), are defined as \(\log_{e}x\) and \(x(x+e)\), respectively. What is the value of \(h(f(e^2 ))\)?

Andy works out the inverse of the function \(f(x)=2^{2x+1}\). What would the graph of \(f^{−1} (x)\) look like when he plots it?

What is the domain of the function \(f(x)=\log_{4}(x^2−9)\)?

Determine the inverse of the function \(f(x)=\log_6⁡(x+8)\).

The table below shows the function \(h(x)\).

Another function \(g(x)\) is equal to \(\log_{10}⁡(x)+x^2\). What is the value of \(g(h (2))\)?

The graph below shows the first \(5\) terms of an Arithmetic Progression.

What would be the \(n\)^th term of a Geometric Progression with the same first term \(a\) and with a common ratio \(r\) equal to the common difference \(d\) of the Arithmetic Progression?

(Note: \(n\) takes on integer values \(1,2,3…\) in the formulae below)

The first term of an arithmetic sequence is −8 and the common difference is 3. What is the sum of the first 10 terms of the sequence?

Look at the sequence below.

\(\log_{10}⁡x, \log_{10}⁡x^3 , \log_{10}⁡x^5 , … \)

\(S_n (x)\) is defined as the sum of the first \(n\) terms of the sequence. Work out the formula for \(S_n (10)\).

The table below shows the first 5 terms of a sequence.

Which of the following is the explicit formula for this sequence?

\(ka^x\) and \(mb^x\) are two exponential functions such that \(1 \lt a \lt b \lt 10\) and \(0 \lt m \lt k \lt 1\).

Find the value of \(x\) for which \(ka^x\) is equal to \(mb^x\).