Exponential functions with any base, and exponential equations
Fill in a table of 2^x, see that a base above 1 gives a rising curve and a base between 0 and 1 a falling one, and solve an exponential equation by writing both sides with one base.
- فلسطين: الصف ١٢
- إيران: الصف ١١
- أوكرانيا: الصف ١١
- روسيا: الصف ١١
- ألمانيا: الصف ١٠
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
The exponential function is y = a^x with a positive and a not 1. It works for negative x too: ٢−١ = ١٢ and ٢٠ = ١.
If a > 1 the graph rises from left to right and stays above the x-axis. If 0 < a < 1 it falls; y = (١٢)x is the mirror image of y = ٢x in the y-axis. Both pass through (٠، ١).
To solve an exponential equation write both sides as powers of one number: ٤x = ٨ becomes ٢٢x = ٢٣, so ٢x = ٣.
Common slips: 2^-1 = −2; reading a falling curve as growth; solving 4^x = 8 as 8 ÷ 4.