Math 1 Unit 1

An exponential function is a mathematical function of the form $$y = a(b^x)$$ , where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.

To represent a population decreasing by a percentage, use the formula $$y = P(1 - r)^x$$ , where 'P' is the initial population, 'r' is the rate of decrease (as a decimal), and 'x' is the time period.

Doubling means that the quantity increases to twice its original amount. In mathematical terms, if the original amount is 'A', after doubling it becomes '2A'.

The equation is $$y = 600(0.96)^x$$ .

The formula is $$y = mx + b$$ , where 'm' is the hourly rate, 'x' is the number of hours worked, and 'b' is the initial amount saved or earned.

The equation is $$y = 5x + 60$$ .

Linear growth increases by a constant amount over time, while exponential growth increases by a constant percentage, leading to faster growth as time progresses.

The equation is $$y = 6(2^x)$$ .

Use the formula $$V = V_0(2^d)$$ , where 'V_0' is the initial number of viewers, 'd' is the number of days, and 'V' is the total viewers after 'd' days.

After 4 days, the number of viewers will be 1920.