Write down and simplify all the terms in the expansion of (1+3x)6.Using your results to estimate the value of (0.97)6correct to four decimal places

Step-by-step explanation:

Given

Solving (a): Expand

To do this, we make use of pascal triangle

When the exponent is 6, the factors are: 1, 6, 15, 20, 15, 6 and 1

As a rule, the exponent of 1 will start from 0 and then increase by 1 in each term while the exponent of 3x will start from 6 and then decrease by 1 in each term.

So, we have:

Expand

Solving (b): (0.97)^6

Rewrite as:

Express -0.03 as 3 * -0.01

So, by comparing:

and

Recall that:

This gives:

Using a calculator

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answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.